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Current and Upcoming Events⌗
Geometry and Topology of Surfaces⌗
Date: June 22, 2026
Location: Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
https://math.gsu.edu.tr/gt2026/
The 22nd International Conference on Fibonacci Numbers and Their Applications⌗
Date: July 06, 2026
Location: Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
https://math.gsu.edu.tr/fibo22/
Past Events⌗
2026⌗
Departmental Seminar - Keremcan Doğan, Gebze Technical University⌗
Date: May 06, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Exceptional Drinfel’d Algebroids and Rackoids
Abstract: String and M-theories dictate new symmetry notions that are absent in point-particle theories. The generalized geometry program extends usual differential geometry in a suitable manner to explain one class of these new symmetries, known as T-duality. In particular, Poisson-Lie T-duality can be understood as arising from different decompositions of the Drinfel’d double of a Lie bialgebra, which is itself a Lie algebra. Extending this to the algebroid setting leads to Drinfel’d doubles of Lie bialgebroids, which are Courant algebroids. In order to explain another class of new symmetries, called U-duality, one needs to further extend these notions. In one of our recent works, we extended Lie bialgebroids and their Drinfel’d doubles to a set-up in which the vector bundles are not dual in the usual sense, and we introduced bialgebroids and their Drinfel’d doubles via a calculus framework on algebroids. In this talk, we use this framework to introduce and construct a specific type of algebroid, which we call exceptional Drinfel’d algebroids. We prove that these are algebroid versions of exceptional Drinfel’d algebras, which have recently been defined in the physics literature in order to extend the Lie bialgebra/T-duality relation to the U-duality case; hence the name. We provide a mathematically rigorous framework to describe these algebras and their algebroid versions in a frame-independent manner, where we use Nambu-Poisson structures and their certain generalizations. Moreover, we introduce exceptional Drinfel’d rackoids, which are global versions of exceptional Drinfel’d algebroids, analogous to the relation between a Lie group and its Lie algebra. As examples, we focus on the $SL(5)$ and $E_{6(6)}$ cases; for the latter we also use another extension called proto bialgebroids, where $H$- and $R$-fluxes are present. Join with Google Meet: https://meet.google.com/cuo-tuyk-hte Or dial: (US) +1 915-247-5177 PIN: 224480191# Learn more about Meet at: https://support.google.com/a/users/answer/9282720
Departmental Seminar - Begüm Ateşli, İTÜ⌗
Date: April 08, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: On the Structural Foundations of Lie Algebroids and Their Higher Analogues
Abstract: This talk is concerned with the structural theory of Lie algebroids and 3-Lie algebroids. After reviewing the basics of Lie algebroids and their connection with Poisson geometry, we introduce a coupling construction based on mutual actions and cocycle terms that produces a Lie algebroid structure on the direct sum of two vector bundles. This bicocycle double cross product construction yields a unified framework for several geometric extensions. We then discuss the analogous construction for 3-Lie algebroids. In the final part of the talk, we explain how a 3-Lie algebroid can be constructed from a given Lie algebroid by using differential operators, Lie and 3-Lie connections, and curvature operators. We also indicate how Poisson Lie algebroids fit into this picture, leading to a Poisson 3-Lie algebroid structure.
Mini Cours - Salah Mehdi, Université de Lorraine⌗
Date: March 26, 2026 at 08:00
A Matrix Centered Introduction to Lie Groups and Lie Algebras - Part 2
Departmental Seminar - Salah Mehdi - Lorrent University, France⌗
Date: March 25, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: From Numbers to Spectrum: A guided ramble through the Langlands Program and Locally symmetric spaces
Abstract: Robert Langlands, a Canadian mathematician, introduced in the late 1960s a remarkable set of conjectures aimed at unifying various areas of mathematics, including number theory, geometry, and spectral analysis. Since then, the Langlands program has been at the forefront of intense research, inspiring several Fields Medals and other prestigious awards. In this talk, designed to be accessible to a broad audience, I will first outline the key ideas and motivations behind Langlands’ unifying program, and then present some recent results on locally symmetric spaces, highlighting how they fit into the broader landscape of Langlands conjectures and representation theory. Some of these results come from joint work with Martin Olbrich.
Mini Cours - Salah Mehdi, Université de Lorraine⌗
Date: March 24, 2026 at 12:00
A Matrix Centered Introduction to Lie Groups and Lie Algebras - Part 1
Visite de Salah Mehdi, Université de Lorraine⌗
Date: March 23, 2026
Visite de Cedric Villani⌗
Date: March 23, 2026
Departmental Seminar: Cem Yetişmişoğlu, Istanbul Medipol University⌗
Date: March 18, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Graded manifolds and their applications in physics
Abstract: In this talk we will define (Z/2Z)-graded manifolds, and certain geometrical structures on them. We will then focus on two applications in which these manifolds appear in physics literature. In the first one, we will be talking about how discrete systems, their dynamics, and their measurements can be described by a generalization of symplectic graded manifolds (math-ph:2311.05711). In the second application, we will be talking about how such manifolds appear in formulations of algebroids and their Drinfel’d doubles which encode symmetries of stringy geometries (hep-th:2409.11973)
Matematik Bölümü Genel Semineri - Tekin Dereli - Özyeğin Üniversitesi, Koç Üni. (Emeritus)⌗
Date: March 04, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye - Aydın Doğan Conference Room
Başlık: 21. Yüzyılda Einstein’ın izinden gidebilecek miyiz?
Özet: Einstein’in genel görelilik teorisi 1916 yılına dayanmaktadır ve kütleçekimi anlayışımız için dinamik bir uzay-zaman yapısı çerçevesinde matematiksel bir temel sağlar. Teorinin en çarpıcı öngörüleri arasında kütleçekimsel dalgaların varlığı, genişleyen Evren modelleri, kara deliklerin gerçekliği yer almaktadır. Nitekim bu konuların önemi, son on yılda üç Nobel Ödülü kazanarak kanıtlanmıştır. Bu durum, söz konusu başlıkların gelecek nesil fizikçilerin temel çalışma alanları olacağına dair kuvvetli bir göstergedir. Öncü bir ülke olarak bu çalışmalara neden ve nasıl katılmamız gerektiğine dair birkaç söz söyleyeceğiz.
Departmental Seminar: Öznur Turhan⌗
Date: February 11, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Bekka's (c)-regularity condition and families of line singularities with constant Lê numbers
Abstract: We show that the natural stratifications arising from certain deformation families of line singularities with constant Lê numbers satisfy Bekka’s (c)-regularity condition. As a corollary, we obtain that these families are topologically equi-singular. Similar results for families of isolated singularities were established by Abderrahmane. This is a joint work with Christophe Eyral.
2025⌗
Departmental Seminer: Sibel Şahin (Mimar Sinan University)⌗
Date: December 17, 2025 at 12:00
Title: Approximation Numbers of Differences of Composition Operators
Abstract: In this talk we will consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H2(D). The component structure of bounded
composition operators is a widely studied area and in order to understand whether two composition operators belong to the same component, it is important to understand how their difference behaves (compact, bounded etc.). One of the key elements in understanding the
behavior of an operator is to consider its approximation numbers since it gives us the information about how much our operator differs from a bounded/compact one. During the talk we will mention how we can combine these two topics in operator theory and how one can obtain optimal upper and lower bounds for approximation numbers of differences using classical invariants like Bernstein and Gelfand numbers and specific choices of Blaschke products from the underlying function space.
References
[1] G. Lechner, D. Li, H. Queff ́elec, L. Rodriguez-Piazza : Approximation numbers of weighted composition operators. Journal of Functional Analysis 274, 1928–1958 (2018).
[2] J. Moorhouse, C. Toews : Differences of composition operators. Contemporary Mathematics 321, 207–213 (2003).
[3] H. Queffelec, K. Seip : Decay rates for approximation numbers of composition operators.
Journal d’Analyse Mathématique 125, 371–399 (2015).
Remark: First researcher (a) is supported by The Scientific and Technological Research
Council of T ̈urkiye (TUBITAK)-2219 International Postdoctoral Research Fellowship Program (Project no: 1059B192301690).
Departmental Seminer: Yorgo Şenikoğlu (Galatasaray Üniversitesi)⌗
Date: December 03, 2025 at 12:00
Location: Room H307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Scattering of massive neutrino test elds from a gravitational pulse
Abstract: Linearized Einstein-Weyl equations are solved precisely in the context of
sandwich gravitational waves. The neutrino’s energy-momentum depends
on the geometry and composition of the gravitational pulse when it is scattered.
Since the background remains unchanged at the test field level, the
neutrino’s energy density will exhibit fluctuations between positive and
negative extremes when traversing the sandwich wave. These variations
could provide insights into the behavior of models concerning neutrino
oscillations.
Yıldırım Akbal⌗
Date: June 18, 2025 at 13:00
Location: Galatasaray Üniversitesi, Ortaköy, Ciragan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Towards a Foundational TS Model
Abstract: In this talk we will look at a series of foundational time series (TS) models. Starting with a discussion of classical approaches like ARIMA and their limitations, we will explore why traditional machine learning models often fail in this domain. Introducing “One-for-All”, a model designed to address many of these challenges, we highlight its unique features and training procedure, while addressing its limitations. Finally, we propose some ideas and share some insights to enhance the model’s capabilities over long horizons, ensuring robustness and accuracy in extended time series forecasting.
Pascale Roure (Yıldız Teknik Üniversitesi)⌗
Date: May 14, 2025 at 12:00
Location: Room H306, Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: “A World of Probability”. Hans Reichenbach’s epistemological contribution to logical empiricism in the 1930s.
Abstract: After his dissertation on “The concept of probability in the mathematical representation of reality” (Erlangen 1915), Hans Reichenbach elaborated a probabilistic theory of knowledge aimed at solving the problem of induction, first in the context of the Berlin Group of logical empiricism and after 1933 during his 5-years stay at Istanbul University. His innovative approach among the European empiricists at that time was based on a logic of probability, understood as a logic with a continuous scale of truth-values, in terms of which the two valued logic appears as special case. Reichenbach’s probabilistic theory of knowledge gave rise to vivid discussions in the mid 1930s, that led him to criticize harshly the “positivism” he associated with some representatives of the Vienna Circle, as formulated in his work Experience and Prediction (1938). Drawing on Reichenbach’s writings on the concept of probability and its epistemological significance, my presentation aims to clarify the idiosyncrasy of his reflections and their role in the early development of an analytical philosophy of science or, in Reichenbach’s words, of a “method of analysis of science” (wissenschaftsanalytische Methode).
A. Begüm Bektas (Sloan Kettering Institute)⌗
Date: April 16, 2025 at 12:00
Location: Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Learning with Kernels: Interpretability, Efficiency, and Applications to HighDimensional Data
Abstract: Inthis talk, I will give a brief introduction to learning with kernels, afundamental area in machine learning. I will then present an overview of tworelated publications from my work. The first focuses on multiple kernellearning (MKL), which combines multiple kernel matrices and a domain relatedinformation source in an optimization model. I will discuss how this method canperform well on high dimensional and highly correlated data, how it can achieveinterpretability, and how it can yield improved outcomes using only one tenthof the data. If time allows, I will also address a well-known limitation ofkernel methods, namely the high computational cost, and introduce MultipleApproximate Kernel Learning, a novel approach that provides scalability and efficiencyby using approximated matrices in place of full kernel matrices in MKL.
Mini cours: Mathématiques pour ChatGPT et les réseaux de neurones - Arnaud Bodin, Univ. de Lille⌗
Date: February 27, 2025 at 13:00
Mini cours: Mathématiques pour ChatGPT et les réseaux de neurones - Arnaud Bodin, Univ. de Lille⌗
Date: February 26, 2025 at 13:00
Mustafa Topkara (Mimar Sinan Güzel Sanatlar Üniversitesi)⌗
Date: February 26, 2025 at 12:00
Location: Room h307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Limits in the Mapping Class Groupoid of Surfaces
Abstract: One way to investigate surfaces is through their triangulations or, equivalently, the dual ribbon graphs (the ‘modular graphs’) and an operation that relates them (the ‘flip’). In this talk, we will discuss the effect of flips on the ‘infinite punctures’ of a surface and explore possible ways to take limits of such flips.
Cheikh LO - Anta Diop University of Dakar⌗
Date: February 19, 2025 at 12:00
Location: Galatasaray Üniversitesi Ortaköy; H306
Title: ON CHARACTERISTICS OF ISOMETRIES IN HYPERBOLIC GEOMETRY
Abstract: In the first time of the talk we present characteriza-tions of isometries of hyperbolic plane by using some geometric objects. More precisely we show that the curves of constant geodesic curvature-preserving maps are isometries. In the second time we highlight the difference between geodesics and horocycles by showing that an abstract automorphism of the geodesic graph is induced by an earthquake map while that of a horocycle graph is induced by an isometry. Join with Google Meet: https://meet.google.com/mia-pyfu-iqz Or dial: (US) +1 401-753-9621 PIN: 107158657# Learn more about Meet at: https://support.google.com/a/users/answer/9282720
Visiteur: Arnaud Bodin, Université de Lille⌗
Date: February 19, 2025
Burak Kaya (Ortadoğu Teknik Üniversitesi)⌗
Date: February 12, 2025 at 12:00
Location: Room h307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Borel distinguishing number
Abstract: In broadest sense, descriptive graph combinatorics is the study of “definable” graphs on Polish spaces that incorporates the descriptive set theoretic point of view into the graph-theoretic point of view. This is usually done by demanding various graph-theoretic objects such as edge relations, colorings, automorphisms to have topological/measure-theoretic properties such as being Borel, projective, continuous, closed and asking to what extent classical results of graph theory generalize to measurable setting. Over the last two decades, numerous interesting results have been proven which demonstrate that this point of view is more than a mere specialization that lead to fruitful ideas. In the first half of this talk, after recalling some basic descriptive set theoretic notions, we shall give a brief overview of some fundamental results in descriptive graph combinatorics. In the second half of this talk, we will cover some new results regarding Borel distinguishing numbers. The results in the second half are from a joint ongoing work with Onur Bilge.
2024⌗
Athanase Papadopoulos: The earthquake metric on Teichmüller space⌗
Date: December 20, 2024 at 11:00
Location: Galatasaray Üniversitesi, Room H303
I will explain new results on the earthquake metric, an asymmetric Finsler metric on the Teichmüller space of a surface. This is recent work with Yi Huang, Ken’ichi Ohshika and Huiping Pan. I will survey the basic properties of this metric, and explain new properties, including incompleteness, asymptotic distance to the boundary and comparisons with the Thurston metric and the Weil-Petersson metric.
Tınaz Ekim (Boğaziçi Üniversitesi): Theory and Computation of the Defective Ramsey Numbers⌗
Date: December 18, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We investigate a variant of Ramsey numbers called defective Ramsey numbers, introduced by Ekim and Gimbel in 2013, where cliques and independent sets are generalized to k-dense and k-sparse sets, both commonly called k-defective sets. Following some defective parameters in general graphs, we focus on the computation of defective Ramsey numbers in some restricted graph classes: cographs, chordal graphs, bipartite graphs, perfect graphs, split graphs, cacti, and triangle-free graphs. We adopt a two-fold approach to tackle defective Ramsey numbers. We provide direct proofs using structural graph theory. When this technique falls short in obtaining new values of defective Ramsey numbers, we use efficient graph enumeration techniques for structured graphs.
René Cori (Institut de Mathématiques de Jussieu-Paris Rive Gauche): Undecidable mathematical statements⌗
Date: December 11, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We all know that in Mathematics, there are statements that can neither be proved nor disproved, such as the axiom of choice or the continuum hypothesis. We also sometimes hear about statements that are “true” but “not provable”. But what does all this mean? Are such statements unavoidable? The notion of “model of set theory” helps clarifying these issues. Of course, we need to specify the meaning of “proving”! Starting with elementary facts about groups, we shall explain what a complete theory is and why Mathematics is hopelessly incomplete.
Özgür Martin (Mimar Sinan Güzel Sanatlar Üniversitesi): How to train your large AI model at a lower cost?⌗
Date: December 04, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
Stochastic gradient descent (SGD) method and its variants constitute the core optimization algorithms that are used for training large-scale machine learning models. These algorithms achieve very good convergence rates, especially when they are fine-tuned for the application at hand. Unfortunately, this tuning process can require large computational costs. For example, GPT-4 (the core machinery of ChatGPT), was trained using trillions of words of text and many thousands of powerful computer chips. The electric bill for the training was over $100 million. Recent work has shown that these costs can be reduced by choosing the learning rate adaptively. We propose an alternative approach to this problem by using a new algorithm based on forward step model building built upon SGD.
Didier Lesesvre (Université Lille): Packing spheres: piling up oranges… and very modern mathematics⌗
Date: November 27, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
Sphere packing is an extremely old problem, yet both widely applied in various domains and very challenging and active mathematically. From unexpected applications to industry to minimizing quadratic forms, from piling up oranges to the mysterious Einstein hat that tiles the plane in an a-periodic way, from very naive questions to the most modern maths (culminating with the groundbreaking achievement of Maryna Viazovska in 2018 to determine the optimal sphere packing in dimensions 8 and 24), I will present some of the developments and ideas behind these questions. These feature in particular beautifully rich mathematical objects: modular forms, which are at the heart of the “modular magic” used by Viazovska, allowing to make the proof of the sphere packing surprisingly accessible.
Mini cours: Formes Modulaires et Formule de Trace de Peterson - Didier Lesevre, Univ. de Lille⌗
Date: November 26, 2024 at 06:00
Mini cours: Formes Modulaires et Formule de Trace de Peterson - Didier Lesevre, Univ. de Lille⌗
Date: November 25, 2024 at 08:00
Visiteur: Didier Lesevre, Université de Lille⌗
Date: November 25, 2024
Sinan Yıldırım (Sabancı Üniversitesi): Adaptive Online Bayesian Estimation of Frequency Distributions with Local Differential Privacy⌗
Date: November 20, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
We propose a novel Bayesian approach for the adaptive and online estimation of the frequency distribution of a finite number of categories under the local differential privacy (LDP) framework. The proposed algorithm performs Bayesian parameter estimation via posterior sampling and adapts the randomization mechanism for LDP based on the obtained posterior samples. We propose a randomized mechanism for LDP which uses a subset of categories as an input and whose performance depends on the selected subset and the true frequency distribution. By using the posterior sample as an estimate of the frequency distribution, the algorithm performs a computationally tractable subset selection step to maximize the utility of the privatized response of the next user. We propose several utility functions related to well-known information metrics, such as (but not limited to) Fisher information matrix, total variation distance, and information entropy. We compare each of these utility metrics in terms of their computational complexity. We employ stochastic gradient Langevin dynamics for posterior sampling, a computationally efficient approximate Markov chain Monte Carlo method. We provide a theoretical analysis showing that (i) the posterior distribution targeted by the algorithm converges to the true parameter even for approximate posterior sampling, and (ii) the algorithm selects the optimal subset with high probability if posterior sampling is performed exactly. We also provide numerical results that empirically demonstrate the estimation accuracy of our algorithm where we compare it with nonadaptive and semi-adaptive approaches under experimental settings with various combinations of privacy parameters and population distribution parameters. (joint w. Soner Aydın)
M. Akif Erdal (Yeditepe Üniversitesi): Equivariant Fibration Categories via Enrichments⌗
Date: November 06, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We first discuss fibration category structures induced by enrichments in symmetric monoidal categories that are also fibration categories. Then we discuss extension of these structures to equivariant context and show that for a group G and a symmetric monoidal category V which is also a fibration category, under mild conditions the category of G-objects in a V-enriched category admits a nontrivial fibration category structure. Lastly we discuss some examples of such fibration categories and applications.
Atabey Kaygun (Istanbul Teknik Üniversitesi): Distributive Laws and Cross Simplicial Groups⌗
Date: October 16, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
There is a way of writing an algebraic structure (a group or an algebra or a category) as a product of two substructures. This is known as a distributive law, and also as a factorization system. After giving examples, I am going to introduce crossed simplicial groups. Crossed simplicial groups are defined by a distributive law between the simplicial category $\Delta$ and a suitable collection of groups. My main aim is to explain how one can extend the notion of ‘simplicial homotopy’ to crossed simplicial groups. We’ll end with a very interesting example coming from Leibniz algebras that are non-skew-symmetric analogues of Lie algebras.
Özlem Ejder (Koç Üniversitesi): Groups, Geometry, Arithmetic and Dynamics⌗
Date: October 02, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
Let a₀ be an integer, let f be a polynomial, and consider the sequence aₙ = f(aₙ₋₁). It is a natural question to ask whether there are infinitely many primes in this sequence. One quickly decides that there are not enough tools at hand to deal with this question and one asks instead about the primes dividing at least one term of the sequence. It turns out that the symmetries of the pre-images of a₀ under the iterates of f play an essential role in the solution of this density question. Motivated by the prime density questions, we study the Galois theory of the iterates of a polynomial (or a rational function). We see fruitful connections between geometry, dynamics, arithmetic, and group theory in this subject. Some of the results presented in this talk are joint work with Y. Kara, E. Özman.
AGCCA (Algebraic Geometry, Computational Commutative Algebra)⌗
Date: June 20, 2024 at 09:00
Location: Galatasaray University
Workshop on Algebraic Geometry and Computational Commutative Algebra. More info: https://math.gsu.edu.tr/agcca/agcca.html
Zeynel Ulusan (Koç University): Exploring the frontier of mathematical reasoning with large language models⌗
Date: May 08, 2024 at 16:00
Location: Galatasaray Üniversitesi, room I222
In mathematics, there are two distinct approaches to reasoning: informal inferences based on simple reasoning and formal derivations through step-by-step proofs. This centuries-old approach to mathematical reasoning has been revolutionized by the advent of computers and symbolic systems. Initially, symbolic systems were developed to construct proofs step-by-step based on formal derivations. Subsequently, with the advent of deep learning, particularly in the form of large language models, we were able to construct neural network-based structures that, like humans, are capable of both inductive and deductive reasoning. It is important to note that both symbolic systems and deep learning systems, in their respective ways, have their own set of successes and failures. This presentation will examine the distinctions between symbolic systems and deep learning-based systems, with a focus on the capabilities of large language models in problem solving, theorem proving, mathematical reasoning, generating new conjectures, and their performance when used with agents. Additionally, it will explore the potential for integrating language models with formal systems and the benefits of this integration.
Sibel Özkan (Gebze Technical University): On Domination Number of Cayley Graphs⌗
Date: April 17, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
A dominating set of ? is a subset D of V , such that every vertex not in D is adjacent to at least one member of D . The domination number ?(?) is the minimum cardinality of a dominating set for ?. An efficient dominating set of ? is an independent subset D of V , such that every vertex not in D is adjacent to exactly one member of D . Observe that if D is an efficient dominating set of ?, then D is also minimum dominating set of ?. There are results on the domination number and finding efficient dominating sets (if exist) on circulant graphs for certain connection sets. Here I will talk about our results on odd-regular circulant graphs and Cayley graphs on different groups by giving the exact domination number when possible or giving a meaningful bound.
Trustworthy AI Workshop⌗
Date: March 29, 2024 at 09:00
Location: Galatasaray University
Workshop on Trustworthy AI. More info: https://math.gsu.edu.tr/trustworthyAI.html
Athanase Papadopoulos (University of Strasbourg): Optimal maps between surfaces⌗
Date: March 22, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I109
I will talk about distance functions between surfaces equipped with metrics, and more especially, I will describe recent works on the Thurston metric and the earthquake metric between hyperbolic surfaces. The work on the earthquake metric is joint work with Yi Huang and Ken’ichi Ohshika. The work on the earthquake metric is joint work with Yi Huang, Ken’ichi Ohshika and Huiping Pan.
Ceren Gürkan (Kadir Has University): How do fluids behave, numerical modelling, new fronts, and applications⌗
Date: February 28, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
Numerical modeling replaces the expensive laboratory experiments if not used parallel to those for developing any technology in science and engineering. Numerical models can be used to understand the behavior of fluids that are essential to our existence and heavily involved in cutting edge technology development. For deeper understanding of the air -hence all aerospace industry-, blood flowing through our veins or spacecrafts traveling to Mars accurate numerical modelling of fluids is vital. This is why technology developers have an unending need for more accurate, faster, and cheaper numerical techniques. The principal component of any numerical model is the partial differential equation that defines the physical phenomena of interest. A fundamental prerequisite for an accurate numerical solution is the generation of a high-quality mesh. Nevertheless, despite continuously growing computer power, mesh generation can still be a challenging task that can easily account for large portions of the computational time. As a possible remedy to the mesh generation challenges, so-called cut discretization methods have gained much attention in recent years. In this talk we will first focus on the basics of fluid modelling and then discover the new fronts and exiting applications where fluids are involved.
Çağrı Diner (Boğaziçi University): Seismic Wave Propagation and Representation of Seismic Sources⌗
Date: February 21, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
In this talk, I will first focus on deriving the wave equation for an elastic medium, followed by a discussion on its Green’s function solution, which incorporates the moment tensor representation of seismic sources. The moment tensor, which is a second-rank tensor, characterizes seismic sources by using the slip direction of an earthquake and the fault’s normal. Moreover, the magnitude of an earthquake is proportionally related to the norm of moment tensor. The structure of the space of moment tensor will be explained, along with the elasticity tensor which is a critical component for the moment tensor’s definition.
Zeynep Hassanzadeh (Istanbul Technical University): Data-driven learning of Lie groups⌗
Date: February 14, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
The main purpose of this talk is to propose a newly developed stochastic Monte Carlo (MC) linear solver for some large-scale modeling problems that require special linear solvers due to the specific characteristics of these types of problems. The newly developed MC method offers an alternative to costly deterministic linear solvers, presenting advantages in computational time and complexity, including superior features such as parallelization capability. In this presentation, we propose employing the stochastic MC method for initial value problems with time-dependent coefficients, resulting in a hybrid numerical-stochastic approach that demonstrates superior efficiency compared to corresponding numerical methods. However, this method exhibits broad applicability to diverse classes of dynamic mathematical modeling problems, particularly at large scales. Additionally, we aim to explore integrating this method into the well-known Adaptive Neural-Fuzzy Inference System (ANFIS), thereby reducing computational complexity in computing the pseudo-inverse matrix within the iterative least square estimator (LSE) sub-method of the main ANFIS algorithm. It is known that the ANFIS method offers a powerful tool for data science analysis across various domains and applications such as predictive modeling, control systems, data fusion decision-making, and so on. Indeed, this method is a versatile tool, but its specific application depends on the data and problem at hand. In this research, we applied three classes of the newly modified ANFIS method, incorporating enhancements to their respective generating function structures. These models were utilized to forecast the daily prices of target fuel products using datasets sourced from the Thomson Reuters Eikon Refinitiv database.
2023⌗
Çağatay Yıldız (University of Tübingen): Data-driven learning of Lie groups⌗
Date: December 27, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Learning meaningful representations via deep neural networks has been an important challenge for computer vision tasks. Auto-encoders have been among the most popular approaches as they are shown to enable so-called disentangled representations. Unfortunately, most auto-encoder-based methods are built upon no or very little inductive biases and lack a theoretical foundation. This (ongoing) work aims to provide insights into how group theory could be beneficial for learning modular representations. Given object-centric datasets, we show how to learn latent matrix Lie groups that model underlying transformations the objects undergo within an auto-encoder framework. The resulting framework learns (almost perfectly) disentangled group actions on toy datasets.
Sylvain Lavau (Aristotle University of Thessaloniki): Singular foliations and Lie ?-algebroids⌗
Date: December 20, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
A singular (or Hermann) foliation on a smooth manifold M can be seen as a locally finitely generated subsheaf of the sheaf of vector fields on M closed under Lie bracket. We show that if this singular foliation admits a resolution consisting of sections of a graded vector bundle of finite type, then one can lift the Lie bracket of vector fields to a Lie ?-algebroid structure on this resolution. The choices entering the construction of this Lie ?-algebroid, including the chosen underlying resolution, are unique up to homotopy and, moreover, every other Lie ?-algebroid inducing the same foliation or any of its sub-foliations factorizes through it in an up-to-homotopy unique manner. We thus call it the universal Lie ?-algebroid of the singular foliation. For a real analytic or holomorphic singular foliation, it can be chosen, locally, to be a Lie n-algebroid for some finite n. We will show that this universal structure encodes several aspects of the geometry of the leaves of a singular foliation, and that it allows to extend to the singular context some notions (e.g. characteristic classes) until now only defined for regular foliations.
Mounir Nisse (Xiamen University Malaysia): Singularities and Rearrangement of Knots Via (Co)amoebas⌗
Date: December 13, 2023 at 15:00
Location: Online
Amoebas (resp. Coamoebas) are the image of analytic subsets of the complex algebraic torus under the logarithmic map (resp. argument map) coordinate-wise. In this talk, we open a way relating deformations of class of germs of complex algebraic plane curves diffeomorphisms to rearrangement of links. Indeed, we realize any torus link as the union of the one-dimensional connected components of the set of critical values ??of the argument map restricted to a complex algebraic plane curve. This gives the first relationship between knot theory and coamoebas theory. Moreover, it gives an explicit description of the topology and geometry of links corresponding to singularities.
Salah Mehdi (University of Lorraine): From Fourier series to asymptotics of characters : a glimpse into Lie theory⌗
Date: December 06, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
In 1822, the French mathematician and physicist Joseph Fourier published his seminal treatise Théorie analytique de la chaleur in which he introduced expansions of periodic functions and solved the heat equation on R. Since then, Fourier series and Fourier transforms have been used successfully and extensively in many areas of fundamental and applied sciences. Harmonic analysis aims to generalize Fourier analysis on topological spaces on which a group acts. Group actions lay at the confluences of Mathematics and Physics, their study is the purpose of representation theory of Lie groups. I will explain the ins and outs of Lie theory, and sketch a few of its many tremendous applications. In particular, I will describe how representation theory relates objects of different nature such as orbits, characters and Dirac operators. These recent results are based on joint work with Pavle Pandzi´c, David Vogan and Roger Zierau.
Türkü Özlüm Çelik (Koç University): Algebraic Curves, Computer Algebra and Integrable Systems⌗
Date: November 22, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Algebraic curves have significant applications in the study of the Kadomtsev-Petviashvili hierarchy, which is a universal integrable system that describes shallow water waves. The corresponding finite-genus solutions are expressed in terms of the Riemann theta function. The theta function degenerates as the curve becomes more singular, leading to soliton and rational solutions. These solutions, in turn, characterize the curves in the moduli space of abelian varieties, thus providing a solution to the Schottky problem. To better understand the bilateral connection, we explore various perspectives in computational algebraic geometry, including transcendental and combinatorial approaches, while also utilizing mathematical software. Our study yields new results and insights, along with future directions for research in this field.
Mark Spivakovsky (Toulouse Paul Sabatier University): On the Casas–Alvero conjecture⌗
Date: November 15, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Let k be a field, d a strictly positive integer and x an independent variable. Let f?k[x] be a monic polynomial of degree d. For i?{1,…,d-1}, let f(i) denote the i-th derivative of f (the i-th Hasse derivative in case char k>0). Assume that for all i?{1,…,d-1} the polynomial f(i) has a non-trivial common factor with f. The Casas–Alvero conjecture asserts that, assuming char k=0, there exists a?k such that f(x)=(x-a)d. If char(k)=p>0, the conjecture is false in general. Let us write CAd,p for the statement “The Casas-Alvero conjecture holds for polynomials of degree d over fields of characteristic p”. The following equivalences are known for each d: CAd,0 holds ?CAd,pholds for some prime number p?CAd,p holds for all but finitely many primes p. A prime number p is said to be a bad prime for d if CAd,p is false. In this talk we will discuss an approach to the conjecture that consists in first proving it for some small degree d, compiling lists of bad and good primes for that d and then deducing the conjecture for all the degrees of the form dpl, where l is a positive integer and d a good prime for d. At the end of the talk we will mention a recent result (joint with D. Schaub) that gives a long (but not exhaustive) list of good primes for each d.
Adam Ouzeri (Galatasaray University): A theoretical and computational framework for upscaling epithelial subcellular dynamics to tissue mechanics⌗
Date: November 08, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Recent observations across various species have revealed a rich phenomenology of epithelial mechanics arising from the active-viscoelasticity and turnover of the actomyosin cortex. However, a link between the subcellular cortical dynamics and the tissue scale response has been lacking in theoretical models of epithelia. For instance, in classical vertex models, a phenomenologically motivated work function governing the vertex dynamics (Alt et al, Philos. Trans. R. Soc. Lond., B, Biol. Sci., 2017) often lacks a direct connection to the microscopic subcellular physics. In this talk, I will present a new formalism, coined active-gel tissue model (AGTM), which bridges the active-gel models of the actomyosin cortex taking into account the active contractility of the cortex, the viscoelastic relaxation due network remodelling and the turnover of its constituents, with vertex-like models at a tissue scale. By solving the active gel on each of the curved faces of a 3D tissue, we show that this unified framework systematically links subcellular cortical dynamics with tissue mechanics, and ties to a common subcellular origin a number of seemingly disconnected dynamical tissue behaviours such as stress relaxation following step-strain manoeuvres (Casares et al., Nat. Mat. 2015, Khalilgharibi et al, Nat. Phys., 2019), buckling and transient buckling upon compression (Wyatt et al, Nat. Mat., 2020), pulsatile contractions during Drosophila dorsal closure (Solon et al, Cell, 2009), spontaneous curling (Fouchard et al, PNAS, 2020) and active superelasticity (Latorre et al, Nature, 2018). This framework is compatible with more elaborate dynamical models of the cytoskeleton, of adhesion complexes and their interaction, and thus serves as a general background for combining more complex multi-species models accounting for regulatory networks and junctional rearrangements, potentially providing a mechanistic understanding of active non-linear response of tissues with cell level resolution.
José Luis Cisneros-Molina (National Autonomous University of Mexico): Indices of vector fields for mixed singularities⌗
Date: October 18, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
A mixed function is a real analytic function f:Cn›C in the complex variables z1,…,zn and their conjugates ¯z1,…,¯zn. In this talk we define an integer valued index for vector fields v with isolated singularity at 0 on real analytic varieties Vf:=f-1(0) defined by mixed functions f with isolated critical point at 0. We call this index the mixed GSV-index and it generalizes the classical GSV-index defined by Gomez-Mont, Seade and Verjovsky, i.e., if the function f is holomorphic, then the mixed GSV-index coincides with the GSV-index. Furthermore, the mixed GSV-index is a lifting to Z of the Z2-valued real GSV-index defined by Aguilar, Seade and Verjovsky. As applications we prove that the mixed GSV-index is equal to the Poincar'e-Hopf index of v on a Milnor fiber. If f also satisfies the strong Milnor condition, i.~e., for every ?>0 (small enough) the map f?f?:S?\Lf›S1 is a fiber bundle, we prove that the mixed GSV-index is equal to the curvatura integra of f defined by Cisneros-Molina, Grulha and Seade based on the curvatura integra defined by Kervaire.
Teichmüller Theory Workshop (Adana)⌗
Date: February 03, 2023 at 09:00
Location: Adana
Workshop on Teichmüller Theory. More info: https://math.gsu.edu.tr/adanaTM.html
2022⌗
Elif Üsküplü (University of Southern California): TBA⌗
Date: December 14, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Şafak Özden (Tulane University): TBA⌗
Date: December 07, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Mesut Ürün: TBA⌗
Date: November 30, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Jose Seade (National University of Mexico (UNAM)): TBA⌗
Date: November 23, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Figen Öztoprak Topkaya (Istanbul Technical University): TBA⌗
Date: November 16, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
TBA: TBA⌗
Date: November 09, 2022 at 16:00
Location: Galatasaray Üniversitesi, room H304
TBA
Daniel Massart (Université de Montpellier): TBA⌗
Date: November 09, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Soner Aydınlık (Doğuş University): Nonlocal Vibration Analysis of 3-D Plates Using Riesz-Caputo Fractional Derivative⌗
Date: November 02, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
In this study, nonlocal vibration analyzes of 3-D plates modeled are performed with the help of fractional mechanics. The Riesz-Caputo fractional derivative is used to define nonlocality without using kernel functions. The frequency spectrum and mode shapes of the plates are investigated for different fractional derivative orders ($\alpha$) and different length scale parameters (l). The main contributions of these studies are that the nonlocal approach considering fractional analysis give results closer to the experimental results than the classical theory.
Ferhat Kürüz (Istanbul Gelişim University): On a special family cyclic codes and their applications⌗
Date: October 26, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
Coding theory is a field that allows us to construct methods to transfer and store data in a way that can detect and correct corruptions that may occur during the transmission process. Algebraic coding theory uses algebraic structures to construct these methods. Cyclic codes, which are very useful due to their algebraic properties, have a central importance in algebraic coding theory. m-adic residue codes are a type of codes that generates cyclic codes with the help of residue classes. After briefly talking about algebraic coding theory, I will describe cyclic codes and m-adic residue codes. Then, after briefly summarizing the DNA codes, I will explain the relationship between m-adic residue codes and these codes. Finally, I will talk about quantum codes and explain their relationship with m-adic residue codes.
Tülay Ayyıldız Aksoy (Karadeniz Technical University and Istanbul Technical University): Polynomial Real Root Certification using Hermite Matrices over Q⌗
Date: October 12, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
Polynomial systems can be solved reliably using numerical homotopy methods. These methods return numerical approximations to solutions, and all the implementations validate the solutions heuristically. Therefore, the output, the approximate solutions of polynomial systems are not certified. Even though the approximate solutions work well in practice, they cannot be used in critical applications, especially in pure mathematics or when high precision is needed (e.g. Surgical Robot arm applications). Let I be a zero dimensional and radical ideal generated by m polynomials with exact rational coefficients. Assume that we are given approximations for the common exact roots. In this talk, we show how to construct and certify the rational entries of Hermite matrices for I from the approximate roots. Furthermore, we represent a method to certify the real roots of the given polynomial system using the signature of Hermite matrices.
Athanase Papadopoulos 65th Birthday Conference⌗
Date: June 20, 2022 at 09:00
Location: Galatasaray University
Conference celebrating Athanase Papadopoulos’s 65th Birthday. More info: https://math.gsu.edu.tr/websitesiathanpapa.html
Asgar Jamneshan (Koç University): The structure of arbitrary Conze-Lesigne systems⌗
Date: May 25, 2022 at 15:00
Location: TBA
Conze-Lesigne systems are abelian measure-preserving dynamical systems which are isomorphic to their second Host-Kra-Ziegler factors. These factors (and their versions of higher order) are relevant ?in multiple recurrence and related topics in additive combinatorics (e.g. Szemeredi’s theorem). In this talk, we present a structure theorem for Conze-Lesigne systems for actions of an arbitrary countable discrete abelian group, describing such systems as an inverse limit of translational systems G/L, where G is a locally compact nilpotent group of nilpotency class 2 and L is a lattice in G. Such structure theorems were previously known in the important special cases of finitely generated abelian groups by work of Conze and Lesigne and direct sums of finite fields by work of Bergelson, Tao, and Ziegler. We will review some of this literature by way of illustrating examples. If time permits, we present an application of our structure theorem to give a qualitative proof of the inverse theorem for the Gowers U^3-uniformity norm of an arbitrary finite abelian group via a correspondence principle. This talk is based on work jointly with Shalom and Tao. I will introduce and motivate the topic to a general mathematical audience in the first half of my talk.
Yasemin Kara (Boğaziçi University): Solving Fermat Type Equations Via Modular Approach⌗
Date: May 11, 2022 at 15:00
Location: TBA
The asymptotic Fermat conjecture(AFC) states that for a number field K and for sufficiently large primes, the equation x^p+y^p+z^p=0 has only trivial solutions. The strategy which is referred as the “modular method” to solve the Fermat equation, used by Wiles in his famous proof, can be adapted to attack AFC and its several different generalizations. Similar results are quite rare for other Fermat type equations such as x^p+y^q=z^r although the solutions of this equation have been studied over rationals. In this talk, I will mention some recent asymptotic results for the classical Fermat equation as well as some other Fermat type equations over number fields. This talk is based on joint works with Isik and Ozman.
Kevin Buzzard (Imperial College London): Teaching proofs to a computer⌗
Date: April 20, 2022 at 15:00
Location: Microsoft Teams
We all know about computer algebra packages like Maple or Matlab, which can be used to do calculations. But there are other computer programs called things like Coq or Lean or Isabelle/HOL, which can be used to check or generate mathematical proofs. Such systems have existed for decades but it is only recently that the research mathematical community have begun to take them seriously. I will give an overview of what has been happening over the last few years, and also why I think it might begin to matter to our community. I don’t think that computers will be automatically proving the Riemann Hypothesis any time soon, but I do think that maybe they will soon be able to help us with our research, in areas where Maple and Matlab are no use. I will assume the audience has a basic mathematical background but I will not assume any knowledge of computers or computer proof systems.
Hatice Boylan (Istanbul University): The sum of all natural numbers, prime numbers and other mysteries⌗
Date: April 06, 2022 at 15:00
Location: Microsoft Teams
What is the value of the infinite sum 1+2+3+4+…, how can we make sense of it and why should we care? In these considerations we end up at some point at the Riemann zeta function which encodes the mysteries of the distribution of primes. We explain how Riemann deciphered part of this encoding and mention some relations to modern physics.
Ezgi Kantarcı Oğuz (Boğaziçi University): Rank Polynomials of Fence Posets are Unimodal⌗
Date: March 23, 2022 at 15:00
Location: Galatasaray University, room H306
We prove a conjecture of Morier-Genoud and Ovsienko that says that rank polynomials of the distributive lattices of lower ideals of fence posets are unimodal. We do this by introducing a related class of circular fence posets and proving a stronger version of the conjecture due to McConville, Sagan and Smyth. We show that the rank polynomials of circular fence posets are symmetric and conjecture that unimodality holds except in some particular cases. We also apply the recent work of Elizalde, Plante, Roby and Sagan on rowmotion on fences and show many of their homomesy results hold for the circular case as well (joint work with Mohan Ravichandran).
Zehra Bilgin (Fatih Sultan Mehmet Vakıf University): TBA⌗
Date: March 09, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H306
(Abstract not available in text)
Fatma Çiçek: TBA⌗
Date: February 23, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H306
(Abstract not available in text)
Ahmad Rafiqi (Galatasaray University): Characterizing Abelian differentials and pseudo-Anosov maps as permutations of integers⌗
Date: January 26, 2022 at 15:00
Location: Galatasaray University, room A324
Thurston’s theory of homeomorphisms from a compact surface of genus greater than one to itself, classifies such maps (and their mapping classes) into three types: periodic, pseudo-Anosov, or reducible - where the surface decomposes into pieces on which the restrictions of the map are either periodic or pseudo-Anosov. The pseudo-Anosov case is thus of great interest in studying these maps. In this case, an integrable quadratic holomorphic differential exists on the surface w.r.t. a Riemann surface structure. When the foliations of the quadratic differential are orientable, namely when there is an Abelian differential preserved by the map, we will characterize the structure of the surface and the pseudo-Anosov map in terms of a permutation of integers.
Türkü Özlüm Çelik (Boğaziçi University): Algebraic Curves to their Jacobians and back⌗
Date: January 12, 2022 at 15:00
Location: Microsoft Teams
We approach the Torelli problem of reconstructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design machinery to solve this problem effectively, which builds on methods in numerical algebraic geometry. We verify these methods via numerical experiments with curves up to genus 7. This is joint work with Daniele Agostini and Demir Eken.
2021⌗
Özlem Ejder (Boğaziçi University): Isolated points on Modular Curves⌗
Date: December 29, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
One of the oldest areas of mathematics is the study of integer or rational solutions to polynomial equations with integer coefficients and it remains active till today. The most natural question we can ask about such an equation is whether its set of rational solutions is finite or infinite. This can be determined by the genus of the curve defined by such equations. In particular, if the genus is greater than one, there are finitely many rational points on a curve. What happens when one allows for solutions involving square-roots of integers or cubic roots? Perhaps in general all complex numbers that are roots of a degree d polynomial? We call such solutions of degree 2,3 or d in general. In this talk, we will discuss when a curve has infinitely many degree d points focusing particularly on points on modular curves
Gönenç Onay: TBA⌗
Date: December 22, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
(Abstract not available in text)
Can Ozan Oğuz (Gebze Technical University): Induction and restriction on symmetry groups of binary trees⌗
Date: December 08, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
Symmetry groups of binary trees are isomorphic to iterated wreath products of symmetric groups of order two. In our collaboration with Mee Seong Im, our aim was to describe the relations between induction and restriction on representations of this tower of groups, which embed into each other. Even though we didn’t get a full description of the relevant category, we have partial results concerning the vector space and algebra structure of certain hom spaces. In the talk I will focus on the origin of the problem and various approaches we found helpful during our research.
2020⌗
Monodromy and Hypergeometric Functions Workshop⌗
Date: February 17, 2020 at 09:00
Location: Galatasaray University
Workshop on Monodromy and Hypergeometric Functions. More info: https://math.gsu.edu.tr/2020workshopmonodhypergeom.html
2019⌗
Mini School on Singularities of Surfaces⌗
Date: November 06, 2019 at 09:00
Location: Galatasaray University
Mini School on Singularities of Surfaces. More info: https://math.gsu.edu.tr/Nov2019.html
Journées Arithmétiques 2019⌗
Date: July 01, 2019 at 09:00
Location: Istanbul
Journées Arithmétiques international conference. More info: https://math.gsu.edu.tr/JA2019.html
Nigar Tuncer (Bilgi University, İstanbul): The Principles of Topofold: designed modular biomolecular folds⌗
Date: May 08, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Biopolymers are able to form many complex nanostructures. Nature uses folded proteins as carriers of functional properties or interactions with other biopolymers. Bacause of complex interplay of interactions it is very hard to predict the tertiary structure from the primary structure. Designing completely new protein fold is even more challenging. In this talk, we overview a self-assembly strategy for single-chain polypeptide tetrahedron assembled from coiled-coil segments.
İstanbul Matematik Festivali 2019⌗
Date: May 04, 2019 at 09:00
Location: Istanbul
İstanbul Mathematics Festival - outreach event for students and public. More info: https://math.gsu.edu.tr/festival2019
José Cidade Mourao (Instituto Superior Tecnico, Lisbon): Complex Symplectomorphisms, Kahler Geodesics and Representation Theory.⌗
Date: April 19, 2019 at 10:00
Location: Galatasaray Üniversitesi FEF 8
The geodesics for the Mabuchi metric on the space H of Kahler metrics on a compact symplectic manifold M correspond to solutions of a homogeneous complex Monge-Ampere (HCMA) equation. The space H is an infinite dimensional analogue of the symmetric spaces of noncompact type G_C/G for compact Lie groups G. In H the role of G is being played by the group of Hamiltonian symplectomorphisms. I will describe a method for reducing the relevant Cauchy problem for the HCMA eq with analytic initial data to finding a related Hamiltonian flow followed by a “complexification”. For Hamiltonian G-spaces, with G-invariant Kahler structure, the geodesic corresponding to the norm square of the moment map or its Hamiltonian flow in imaginary time (= gradient flow for the changing metric following the geodesic) leads to the convergence of the holomorphic sections to sections supported on Bohr-Sommerfeld leaves. For M=T*G, starting from the vertical or Schrodinger polarization, one obtains the Segal-Bargman-Hall coherent state transform.
Lorenzo Ramero (Université de Lille): Les presques anneaux⌗
Date: April 10, 2019 at 15:30
Location: Galatasaray Üniversitesi FEF 8
Les presques anneaux trouvent leur origine dans les travaux de Faltings sur la théorie p-adique de Hodge, où ils fournissent un outil clé pour le preuve de son théorème de presque pureté, qui à son tour est une profonde généralisation d’une observation remontant à l’rticle fondateur de Tate sur les groupes p-divisibles. Plus recemment, les presques anneaux sont devenus le socle sur lequel Scholze a bati sa théorie des anneaux et espaces perfectoides, l’une des plus spectaculaires trouvailles de la géométrie arithmétique des dernières années. Dans mon exposé j’introduirai les presques anneaux et j’essayerai d’expliquer comment ils sont utilisés dans la théorie p-adique de Hodge et dans la théorie des espaces perfectoides.
Pierrette Cassou-Noguès (Université de Bordeaux): Structure de l’arbre à l’infini d’un polynôme à deux variables⌗
Date: April 10, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Il s’agit de classifier les polynômes à l’aide de la structure de leur arbre à l’infini. Après avoir rappelé la notion d’arbre àl’infini d’un polynôme àdeux variables, nous introduisons des structures simples dans cet arbre, que nous appelons des peignes. Le résultat principal que nous énonçons est le fait que le nombre de peignes est inférieur ou égal à 1+2g, où g est le genre de la courbe générique. Dans le cas des polynômes rationnels, à l’origine de cette étude, on obtient un arbre qui consiste en un seul peigne. A la fin de l’exposé, nous étudions le cas où il existe des dicritiques de degré 1 et nous retrouvons les arbres des polynômes rationnels simples. (travail commun avec Daniel Daigle, Université de Ottawa)
Hakan Ayral (Galatasaray Üniversitesi): Convolutional, Recurrent and Deep Neural Networks⌗
Date: March 20, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Deep Neural Networks are artificial neural networks with a specific topology belonging to a family of such topologies. Use of many layers with gradually decreasing number of neurons, and use of some specialized prediction and training methods are characteristic of DNNs. Prominent differences between regular ANNs and DNNs consist of highly increased use of layers in specific arrangements, use of specific nonlinear (i.e. ReLU), convolutional or lossy maps to link these layers, and use of specific algorithms (i.e. regularization) to prevent otherwise unexpected problems (i.e. vanishing/exploding gradients) during training. For feature extraction and transformation, each layer uses the output from the previous layer as input in order to learn multiple levels of representations that correspond to different levels of abstraction which forms a hierarchy of concepts. Each layer learns to transform its input data into a slightly more abstract and composite representation; deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning architectures are often constructed with a greedy layer-by-layer method. Deep learning models are vaguely inspired by information processing and communication patterns in biological nervous systems, but they have too many structural and functional differences from biological brains, which make them incompatible with neuroscience evidences. (latter is a separate field called biologically plausible Spiking Neural Networks) The “deep” in “deep learning” refers to the number of layers through which the data is transformed. Deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output; hence it describes potential causal connections between input and output. For feedforward NNs, the depth of the CAP is that of the network; for recurrent NNs a signal may propagate through a layer multiple times, thus CAP depth is potentially unlimited. DNNs are interpreted in terms of the universal approximation theorem and probabilistic inference: For DNNs the universal approximation theorem concerns with information holding the capacity of bounded width, unbounded depth networks. It’s been proven that a DNN satisfying some lower bound constraint on layer width can approximate any Lebesgue integrable function. (Lu, Z. et al., 2017 The Expressive Power of Neural Networks) The probabilistic interpretation features inference and optimization concepts; it considers the activation nonlinearity as a cumulative distribution function. This interpretation led to the introduction of dropout as regularizer in NNs.
Camille Plénat (Aix Marseille Université): Toric embedded resolutions of simple singularities via jet schemes⌗
Date: March 06, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
(Joint work with H. Mourtada) Abstract: One of the aim of Nash’ paper on the arcs spaces (1968) was to understand res- olutions of singularities via the arcs living on the singular variety; in particular he wanted to give a one to one correspondence between families of arcs and es- sential exceptionnal divisors. J.Fernandez de Bobadilla and M.Pe Pereira (2011) have shown that such a bijective correspondence for abstract resolutions of singular surfaces. But the proof does not give a constructive way to get the resolution from the arcs space. With H.Mourtada, we construct an embedded toric resolution of simple singularities from their jets schemes. It is the result I will discuss in the talk.
Mohammad Sadek (Sabancı University): How long can a curve capture a sequence?⌗
Date: February 27, 2019 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In this talk we consider a number-theoretic question that interrelates two group structures. An arithmetic progression sequence on rational numbers carries a pattern that can be imitated in the universe of algebraic planar curves. We start with introducing algebraic curves, with due attention to elliptic curves, then we discuss some of the aspects of the arithmetic on these curves. We dene what we mean by an arithmetic progression sequence within the globe of algebraic planar curves. We then display some of the old and recent developments in the theory. Specically, we discuss the possibilities for the length of these progression sequences. Finally, we present some open questions that currently intrigue researchers.
Mee Seong Im (United States Military Academy): Almost-commuting varieties with a flag⌗
Date: February 06, 2019 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In the construction of Hamiltonian reductions in symplectic geometry, interesting and rich connections to Hilbert schemes, Calogero-Moser spaces, and rational spherical Cherednik algebras have emerged over the last two decades. A Borel analogue of the classical general linear group construction (realized after a reduction from the cotangent bundle of enhanced Grothendieck-Springer resolutions) potentially opens doors for its connections to isospectral Hilbert schemes, flag Hilbert schemes, and other algebraic varieties, that are important to geometric representation theory, algebraic combinatorics, and quantum topology. Our construction can also be realized by certain quiver flag varieties, appearing in the geometric interplay in quiver Hecke algebras that categorify quantum groups. I will discuss a Borel analogue of the cotangent bundle of the extended general linear Lie algebra, discussing the complete intersection of the zero fiber of a moment map (as conjectured by Thomas Nevins), an enumeration of the irreducible components, and a Borel analog of an almost-commuting scheme appearing in the study of Calogero-Moser systems. No background is necessary and I will give plenty of examples throughout my talk. This is joint with Travis Scrimshaw.
2018⌗
Nermine El Sissi (The American University in Cairo): A Combinatorial Interpretation of the LDU-Decomposition of Totally Positive Matrices and their Inverses⌗
Date: December 19, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Hironori SHIGA (Chiba university): A K3 modular function induced from a simple K3 singularity⌗
Date: December 19, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Bruno Deschamps (Université du Mans): Regarding a weak inverse Galois problem⌗
Date: December 12, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In the works of E. Fried and J. Kollár in 1978 and of M. Fried in 1980, it has been shown that any finite group is the automorphisms group of a finite extension of the field of the rational numbers. This is a positive answer to a weak form of the traditional Inverse Galois Problem of Galois theory, which ask if, whether or not, every finite group G appears as the Galois group of a Galois extension of Q. Since the work of Fried- Kollár/Fried, several advances have been made on this weak form. The most recent is from 2017 and is due to E. Paran and F. Legrand who show that this weak form is actually true on any Hilbertian field. In a recent work with François Legrand, we explain how to provide examples on non-Hilbertian fields. In particular, we show that for any finite group G there exists a field k on which the weak form of the Inverse Galois Problem is true but such that G is not Galois over k. This result thus shows the gap that exists between the Inverse Galois Problem and its weak form.
Mehmet Akif Erdal (Université Bilkent): Realizability of vector bundles by normal bundles of manifolds⌗
Date: November 28, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Given a Poincaré complex $X$, we say a bundle $\xi$ over $X$ is realized by the normal bundle of a manifold $M$, if $\xi$ is pulled back from the normal bundle of $M$ along a homotopy equivalence $X\rightarrow M$. The problem of determining such bundles over an arbitrary Poincaré complex is a difficult problem and is related to classical problems of surgery theory. In this talk, we will discuss some methods of approaching to this problem and talk about solutions for certain cases of $X$. In particular, we will discuss conditions on bundles over $X$ that guarantee they are realized by normal bundles of manifolds, for $X$ belonging to a certain class of homology spheres.
Can Ozan Oğuz (Galatasaray Universitesi): Categorification and Heisenberg algebras⌗
Date: November 21, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Categorification is a recent philosophy that aims to enrich current set-based theories by introducing a new layer of morphisms, hence obtaining a category based theory. A classical example is homology theories that recover Euler characteristic through their dimensions, but offer more since one can talk about morphisms between homology groups now. After an introduction to categorification, we will see how this idea was applied to a Heisenberg algebra, through its connection to representation theory of the symmetric group .
Ezgi Kantarci (Galatasaray Universitesi): A Queer Crystal Structure on Shifted Tableaux⌗
Date: November 07, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Crystal bases were introduced by Kashiwara in his study of the representation theory of quantized universal enveloping algebras. A crystal graph is a directed, colored graph with vertex set given by the crystal basis and directed edges given by deformations of the Chevalley generators and that encodes information about the corresponding representations and their tensor product. In this joint project with Assaf, we define explicit operators on semistandard shifted tableaux and use Stembridge’s characterizationto show that these operators have a crystal structure, giving a new proof that Schur P-polynomials are Schur positive. We then add queer crystal operators (odd Kashiwara operators) that give the semistandard shifted tableaux of a given shape the structure of a connected queer crystal. We also give axioms for queer regular graphs parallel to Stembridge axioms for type A crystals that give a partial local characterization of queer crystals.
François Apery (Université de Haute Alsace): On an algebraic definition of the Boy surface⌗
Date: October 24, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In 1984, I was able to obtain a parametrization of the Boy surface by eliminating the Whitney umbrellas of the Steiner surface using the so-called hyperbolic confluence of pairs of singularities. As a result, the Boy surface appears to be a real algebraic surface of degree six. However, the construction was a mix of geometry, differential topology and singularity theory. In this talk I want to investigate the question in the complex algebraic geometry field. We intend to characterize the Boy surface as an complex algebraic surface subjected to natural conditions.
Muhammed Uludağ: Mapping Class Groupoids, Thompson’s groups and Outer Automorphism Groups of Free Groups⌗
Date: October 10, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We concoct a uniform treatment of mapping class groupoids and Thompson’s groups thereby introducing their hybrid groupoids. As a by-product we obtain a description of the outer automorphism group of free groups as the isotropy group of a groupoid, which extends the mapping class groupoid of Mosher and Penner. We illustrate some arithmetic aspects of these groupoids at the end of our talk.
Mathematical Topics in Quantization Workshop⌗
Date: September 12, 2018 at 09:00
Location: Galatasaray University
Workshop on Mathematical Topics in Quantization. More info: https://math.gsu.edu.tr/2018workshopgeomquant.html
Ozlem Beyarslan: Fields with Virtually Free Group Action⌗
Date: May 02, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
This is joint work with Piotr Kowalski. A G-field is a field, together with an action of a group G by field automorphisms. Our purpose is to give an axiomatization of the theory of “generic”, i.e. existentially closed G-fields. If such axiomatization for the class of existentially closed G-fields exists, we call the resulting theory G-TCF. If G is the trivial group then G-TCF is the theory of algebraically closed fields, ACF. If G is the group of integers, then G-TCF exists and its theory is very well studied ACFA, the theory of algebraically closed fields with a generic automorphism. It is also known that G-TCF exist if G is finite, and G is a finitely generated free group. A natural generalization of finite groups and free groups is the class of virtually free groups. Our main theorem says that, when G is a finitely generated virtually free group, then G-TCF exists. We also give field theoretic propertied of G-fields.
Hussein Mourtada: Arc spaces and partition identities⌗
Date: April 25, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
We will show a link between the arc space (which is an algebro-geomtric object) and the identities of partitions of integer numbers: a partition of a positive integer number is simply a way of writing it as a sum of positive integer numbers. Integer partitions have a long and beautiful history in number theory. The link that we will describe, gives a new point of view on known results and gives new identities.
Michel Coornaert: The Garden of Eden theorem: from Conway’s Game of Life to Arnold’s cat⌗
Date: April 11, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
The Garden of Eden theorem was established by Edward Moore and John Myhill in 1963. It states that a cellular automaton is surjective if and only if it satisfies a weak form of injectivity known as pre-injectivity. In 1999, Mikhail Gromov suggested that the Garden of Eden theorem could be extended to a suitable class of hyperbolic dynamical systems. In this talk, I will discuss the classical Garden of Eden theorem as well as some recent results in the direction indicated by Gromov. This is joint work with Tullio Ceccherini-Silberstein.
Ipek Tuvay: Stable equivalence of Morita type and Scott modules⌗
Date: April 04, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
Let G be a finite group, p a prime number and k an algebraically closed field of characteristic p. Modular representation theory of finite groups aims to understand the blocks of kG which are the indecomposable two-sided ideals of the group algebra kG. To achieve this aim many categorical equivalences between module categories of the block algebras are introduced.Among these, we are concerned with the stable equivalence of Morita type. In this talk after a brief introduction to the subject, the role of Scott modules in this picture will be discussed. Then a recent result with a joint work with S. Koshitani among these lines will be presented.
Valentin Burcea: Formal Holomorphic Embeddings Between BSD-Models⌗
Date: March 21, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
I will be talking about the classification problem for Formal Holomorphic Embeddings between Shilov Boundaries of Bounded and Symmetric Domains.
Mohan Ravichanran: Finite free probability⌗
Date: March 07, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
Free probability, introduced by Voiculescu in the early 1980’s is a general method to study asymptotic statistics of random matrices. It also provides a parallel theory of probability with the notion of independence replaced by so called ‘freeness’. Research over the the last three decades has shown the existence of ‘free’ analogues of results ranging from central limit theorems to the existence of Brownian motion to De Finetti type theorems in free probability. Freeness however does not exist in finite dimensions and as such free probability is inherently qualitative in the results it yields for random matrices.In 2015, Adam Marcus proposed a theory called ‘finite free probability’ that seems capable of providing non-asymptotic results. There are several questions that are wide open in this new setting and I will mention some current work of mine that seems to clarify at least one of them.
2017⌗
Atabey Kaygun: Distributive Laws and Unramified Graph Coverings⌗
Date: December 27, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Distributive laws, also known as “factorization systems,” are useful tools. I will start by few examples, and then explain how an unramified graph covering is equivalent to a pair of groupoids linked together with a distributive law. I will also talk about the beautiful Galois theory behind such coverings. Time permitting, I will comment on the homological ramifications of having such pairs.
İlker Savaş Yüce: Isometries of length 1 in purely loxodromic free Kleinian groups and trace inequalities⌗
Date: December 13, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Hakan Güntürkün: Some Results On Line Arrangements⌗
Date: December 06, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We will review some classical problems and results about line arrangements in the real and complex projective plane. For real arrangements, Sylvester-Gallai and orchard problems, Dirac-Motzkin conjecture and some comments about the solutions will be given. For complex arrangements we will describe nets as well as some special arrangements. We will present Melchior’s and Hirzebruch’s inequalities. Finally, after introducing tropical lines, we intend to present some of our own work on the subject.
Nihat Berker: Chateaubriand, Simone de Beauvoir, MIT, and Augmented Mechanics: Education and Research across 3 Cultures⌗
Date: November 29, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Jean-Louis Verger-Gaugry: Limit Problems in Number Theory, Lehmer’s Conjecture and Dynamical Zeta Functions⌗
Date: November 15, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
To dynamical systems of arithmetical origin are associated dynamical zeta functions. Focus will be given to the Rényi-Parry beta-shift and its use for the problem of minoration of the Mahler measure of algebraic numbers (or of the height). In particular the Conjecture of Lehmer, the Conjecture of Schinzel-Zassenhaus and Dobrowolski’s inequality will be considered.
İlhan İkeda: On the Langlands functoriality principle⌗
Date: November 08, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Let K denote a global field. In the first part of our talk, we shall introduce an unconditional topological group WA_K, which depends only on the global field K,and which is closely related with the hypothetical automorphic Langlands group L_K of K. In the second part of our talk, we shall introduce a new type of parameters and discuss how these parameters are related with the reciprocity and functoriality principles of Langlands.
Romanian-Turkish Mathematics Colloquium II⌗
Date: October 25, 2017 at 09:00
Location: Galatasaray University
Second Romanian-Turkish Mathematics Colloquium - joint meeting. More info: https://math.gsu.edu.tr/2017RT.html
Nicolas Dutertre: Lispchitz-Killing curvatures of semi-algebraic sets⌗
Date: June 07, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We recall the definition of the Lipschitz-Killing curvatures of submanifolds of $R^n$ and of semi-algebraic sets. We give several Gauss-Bonnet theorems for semi-algebraic sets.
Mini Cours: Topologie des singularités réelles⌗
Date: June 06, 2017 at 09:00
Location: Galatasaray University
Mini course (6-7-8 June 2017) on topology of real singularities.
Mini Cours: Les Espaces des Arcs et Résolution des Singularités⌗
Date: June 06, 2017 at 09:00
Location: Galatasaray University
Mini course (6-7-8 June 2017) on arc spaces and resolution of singularities.
Can Deha Karıksız: Hypercyclicity of Weighted Backward Shifts on Spaces of Real Analytic Functions⌗
Date: May 17, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Roland Bacher: How to poison all the big rats⌗
Date: May 03, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We construct a “small” subset of points (locations of poison) wich intersects all convex sets of sufficiently large area (the big rats). We outline the higher dimensional generalization and discuss related open questions. Finally, we present perhaps rapidly a connection with phyllotaxis (the connection is mathematical and not based on the fact that leaves of plants are eaten by rats).
Enver Özdemir: Class number of Real Quadratic Fields⌗
Date: May 03, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In this talk, I will present a relation between the class numbers of imaginary quadratic fields and real quadratic fields. I will talk about prime factors of class numbers of certain quadratic fields and explain how we exploit this to find factors of composite integers.
Mustafa Topkara: Decomposability of Fiber Bundles⌗
Date: April 26, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
A fiber bundle is said to be “indecomposable” if it cannot be expressed as a fiber product of fiber bundles of smaller fiber dimension, and is “stably indecomposable” if its fiber product with any other fiber bundle cannot be decomposed into (i.e. expressed as a fiber product of) fiber bundles of smaller fiber dimension. The talk will be about the relationship between these two concepts.
Oğul Esen: Matching of dynamical systems: With an introduction to Geometric Mechanics⌗
Date: April 19, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
The talk will be consisting of two main parts. In the first one, a gentle introduction to the geometric mechanics will be presented. Accordingly, some basic notions of the theory namely, Lie groups, Lie algebras, Poisson manifolds, and Hamiltonian systems will be summarized. Several examples will be provided. In the second part, we shall address the problem of determining the matched equations of motion of two interacting systems (whose configuration spaces are Lie groups) governing the coupled system starting with the individual equations of motions in Hamiltonian form. The configuration spaces of the systems being Lie groups is imperative here in order to define the mutual actions. We shall present the theory of matched dynamics and particularly write the matched Lie-Poisson equations. It will be shown that the theory of matched dynamics is a generalization of the well-developed semi-direct product theory.
Denis Ibadula: Techniques for computing the Igusa local zeta function of some plain curves⌗
Date: March 15, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
The Igusa local zeta function is a generating function which counts, for a fixed prime number p, the number of solutions of polynomial congruence f(x) ? 0 modulo p, p2, p3, and so on. Naturally, such a quantity bears deep relations to other important mathematical ideas from number theory, algebraic geometry and singularities theory. In this work we explore some computational aspects of the Igusa local zeta function associated to the nondegenerate plane cubics over Qp for p? 2,3.
Esengül Saltürk: Self-Dual Codes Over Local Frobenius Rings⌗
Date: March 08, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Self-dual codes have a rich mathematical theory and they have canonical connections to finite designs and unimodular lattices. We study self-dual and formally self-dual codes over local Frobenius rings of order 16 and give their binary images under a Gray map.
Tropical Geometry in Istanbul⌗
Date: January 15, 2017 at 09:00
Location: Istanbul
Workshop on Tropical Geometry. Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
2016⌗
Murad Özaydın: Noncommutative Algebraic Geometry on a Leavitt Path Algebra of Polynomial Growth⌗
Date: November 30, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Algebraic Geometry classically studies the geometry of sets given as the solutions to polynomial equations via the commutative algebra of “regular” functions on this set. According to the Gelfand-Grothendieck philosophy a commutative ring should be thought of as a ring of functions: Complex valued continuous functions for (locally) compact Hausdorff topological spaces (Gelfand-Naimark duality) where the points of the space correspond to maximal ideals; polynomial functions for affine varieties where we need all prime ideals (with the Zariski topology) to keep functoriality. In Connes’s noncommutative geometry noncommutative rings are also regarded as rings of functions. Now there are several candidates for the “points”: maximal ideals, primitive ideals and simple modules (these are equivalent when the ring is commutative). The general consensus is that there are never enough points (for instance to recover the original ring). Leavitt Path Algebras are constructed from the geometric data of a di(rected )graph G. A theorem of Alahmadi, Alsulami, Jain and Zelmanov says that they have polynomial growth if and only if the cycles of G are mutually disjoint. In this case there seem to be enough points (at least for algebraic quantum spheres) after some tweaking of the spectrum (= space of points). While this is a sequel to the seminar by Ayten Koc, familiarity with that talk is not a prerequisite. Relevant concepts will be (re)defined and graduate students are the target audience.
Ayten Koç: Simple Modules of Leavitt Path Algebras of Polynomial Growth⌗
Date: November 23, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
The first half of this talk will be an introduction to LPAs (Leavitt Path Algebras), in particular their representations. In the second half of the talk I’ll try to indicate the recent classification of the simple modules when the LPA has polynomial growth (joint work with Murad Özaydin). The interesting class of Leavitt path algebras of polynomial growth (i.e. finite Gelfand-Kirillov dimension) include the algebraic Toeplitz/Jacobson algebra and algebraic quantum spheres of every dimension. All the relevant terminology will be dened and explained, the talk is aimed at graduate students.
A Short Course in Diffeology⌗
Date: November 23, 2016 at 09:00
Location: Galatasaray University
Short course in Diffeology (23-24-25-28-30 November, 1 December 2016). More info: https://math.gsu.edu.tr/documents/Programme%20Diffeology%20Oct-Nov%202016.pdf
Zehra Balli: Comparaison Numérique Eléments Finis et Méthode Isogeometrique⌗
Date: November 16, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
L’objectif est de comparer deux méthodes numériques. La méthode d’analyse isogéométrique qui est proposée par Hughes en 2005 permet d’établir une relation étroite et cohérente entre la conception assistée par ordinateur (CAO) et l’ingénierie assistée par ordinateur (IAO).
Konstantinos Tyros: Some Density Ramsey type results⌗
Date: October 26, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
The aim of this talk is to present the density versions of the Hales–Jewett Theorem and the Carlson–Simpson Theorem. The Hales–Jewett Theorem is one of the most representing results in Ramsey theory. Its density version was first proved by H. Furstenberg and Y. Katznelson in 1991 using Ergodic Theory. However, since then, combinatorial proofs have been discovered. The Density Hales–Jewett Theorem has as a consequence Szem ´eredi’s Theorem on arithmetic progressions as well as its multidimensional version. The Density Carlson–Simpson Theorem is an extension of the Density Hales–Jewett Theorem and concerns the space of the left variable words.
Özgür Martin: Disjoint dynamics of linear operators⌗
Date: October 12, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Contrary to popular belief, linear dynamical systems can be chaotic. However, in order to find a chaotic linear map, one needs to work on infinite-dimensional metric spaces. We will make an introduction to Linear Dynamics, which is a new and active branch of Functional Analysis. We will also talk about a recent result of Rebecca Sanders and myself about dense manifolds of disjoint hypercyclic operators.
Extended Differential Calculus Workshop⌗
Date: June 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Extended Differential Calculus. More info: https://math.gsu.edu.tr/diff2016
Arithmetic and Low Dimensional Hyperbolic Spaces Workshop⌗
Date: June 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Arithmetic and Low Dimensional Hyperbolic Spaces. More info: https://math.gsu.edu.tr/2016ahslow.html
Algebra, Geometry and Topology of Singularities Workshop⌗
Date: May 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Algebra, Geometry and Topology of Singularities. More info: https://math.gsu.edu.tr/singularities2016/
Gönenç Onay: To be announced⌗
Date: April 20, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Olcay Coşkun: To be announced⌗
Date: April 13, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Emine Şule Yazıcı: To be announced⌗
Date: March 30, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Oğuzhan Kaya: To be announced⌗
Date: March 23, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Münevver Çelik: To be announced⌗
Date: March 16, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Hironori Shiga: Number theory through the hypergeometric function⌗
Date: March 09, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Lecture Series on Various Aspects of Number Theory⌗
Date: March 05, 2016 at 09:00
Location: IMBM, Istanbul (in collaboration with Galatasaray University)
Lecture series (5-19 March 2016) on various aspects of number theory, with introductory parts accessible to graduate students and non-specialists. More info: https://math.gsu.edu.tr/2016IMBMWorkshop.html
Patrick Iglesias-Zemmour: Diffeology Course (Patrick Iglesias-Zemmour)⌗
Date: March 01, 2016 at 09:00
Location: Galatasaray University
Course on Diffeology by Patrick Iglesias-Zemmour. More info: https://math.gsu.edu.tr/documents/Programme%20Diffeology.pdf
2015⌗
Yusuf Danışman: To be announced⌗
Date: December 23, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Stamatis Pouliasis: To be announced⌗
Date: December 16, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Çagrı Karakurt: To be announced⌗
Date: December 02, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Hugues Randriambololona: To be announced⌗
Date: November 18, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Zafeirakis Zafeirakopoulos: Polyhedral Omega: A new linear Diophantine system solver⌗
Date: November 11, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative approach based on the Omega operator and explicit formulas for its evaluation with geometric tools such as Brion decomposition and Barvinok’s short rational function representations. In this way, we connect two branches of research that have so far remained separate, unified by the concept of symbolic cones which we introduce. The resulting LDS solver Polyhedral Omega is significantly faster than previous solvers based on partition analysis and it is competitive with state-of-the-art LDS solvers based on geometric methods. Most importantly, this synthesis of ideas makes Polyhedral Omega by far the simplest algorithm for solving linear Diophantine systems available to date. This is joint work with Felix Breuer.
Manfred Hartl: To be announced⌗
Date: November 04, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Jose Luis Cisneros: On the topology of real analytic maps⌗
Date: November 04, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
In this talk we describe a fibration theorem for real analytic maps $f:\mathbb{R}^n\to\mathbb{R}^p$ with arbitrary singularities. Now suppose that $f$ satisfies Thom’s property with respect to a Whitney stratification and let $g:\mathbb{R}^n\to\mathbb{R}^k$ be another real analytic map with isolated singularity at the origin in the stratified sense. We give a Le-Greuel type formula which relates the Euler-Poincaré characteristic of the fibres of $f$ and $(f,g)$. When $f$ and $(f,g)$ are isolated complete intersections we construct an integer valued invariant called the curvatura integra which gives the Euler characteristic of the fibres.
Katsampekis Anargyros: Minimal generators of toric ideals associated to numerical semigroups spanned by four positive integers⌗
Date: October 21, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Let a1, . . . , a4 be positive integers with gcd(a1, . . . , a4) = 1, and S =< a1, . . . , a4 > be the numerical semigroup generated by a1, . . . , a4. In this talk we determine a minimal binomial generating set for the toric ideal associated to S. Our approach is based on the detection of those binomials and monomials that have to appear in every system of binomial generators of the toric ideal; these special binomials and monomials are called indispensable in the literature.
Fixed Point Theory and Its Applications⌗
Date: July 01, 2015 at 09:00
Location: Galatasaray University
Conference (July 2015) bringing together experts in fixed point theory, with emphasis on applications across natural sciences, medicine, economics, and engineering. More info: https://math.gsu.edu.tr/fixed-point-theory.html
İlker İnam: Some Problems and A Possible Conjecture On Half-Integral Weight Modular Forms⌗
Date: May 20, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
By the celebrated work of G. Shimura, our knowledge on modular forms of half-integral weight has started to grow. Like in the case of integral weight, they also have arithmetic significance, so both have attracted attention for many years. Recently, one of the breakthrough and very significant results in pure mathematics is the proof of the Sato-Tate conjecture for non-CM modular eigenforms of integral weight (even for Hilbert eigenforms) by Taylor, Barnet-Lamb, Geraghty and Harris. A special case of the Sato-Tate theorem states that signs of coefficients of integral weight Hecke eigenforms are equidistributed. That such should also be the case for half-integral weight forms was conjectured by Kohnen and Bruinier. In this talk, we will discuss the motivation behind this question and explain how the Shimura lift and the Sato-Tate theorem can be exploited to obtain sign equidistribution for certain subsets of the coefficients of half-integral weight eigenforms. Finally, we are interested in the following question: Is it possible state a conjecture like Sato-Tate in the case of half-integral weight modular forms where the question is much more complicated. We will conclude with reporting recent developments on this problem. This is a joint work with S. Purkait (Kyushu), G. Wiese (Luxembourg), S. Arias-de-Reyna (Luxembourg).
Seher Tutdere: On the Torsion-Limit for Algebraic Function Fields⌗
Date: May 13, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk, we first discuss an asymptotic quantity, namely the torsion-limit, for algebraic function fields over finite fields. Then we give some new bounds for the torsion limit of certain towers of function fields over finite fields. Furthermore, using some bounds on the torsion limits, we will give some recent results regarding the construction of arithmetic secret sharing schemes. This is a joint work with Osmanbey Uzunkol.
Mark Spivakovsky: On the Torsion-Limit for Algebraic Function Fields⌗
Date: May 06, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Ekin Özman: The p ranks of Prym varieties⌗
Date: April 29, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This talk is about the relationship between the p-rank of a curve and p-ranks iof the Prym varieties of its cyclic covers in characteristic p>0. Prym variety is a central object of study in arithmetic geometry like Jacobian variety. The goal of the talk is to understand various existence results about Prym varieties such as when g>2, Prym varieties of all unramified cyclic degree ell covers of a generic curve of genus g and p-rank f are ordinary. This is joint work with Rachel Pries
Arzu Boysal: Rational conformal filed theory for pointed stable curves⌗
Date: April 15, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This is a general talk on rational conformal field theory for pointed stable curves. I will give the construction of a rational conformal field theory, and a realization of it in representation theory of affine Lie algebras. Then I will demonstrate how these objects are related to theta functions.
Aydın Aytuna: Parabolic Stein Manifolds⌗
Date: April 01, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for complex manifolds of arbitrary dimension. In the first part of this expository talk, I will compile these notions of parabolicity, compare them and look at some examples. Then I will relate some of these notions to the linear topological type of the Fréchet space of global analytic functions on the given Stein manifold. This will allow us to look at these notions from functional analysis point of view. Finally, I will consider “polynomials” on S-parabolic manifolds and report on some general results about these objects. Most of what I will report in this talk is from joint work with A. Sadullaev.
Jiro Sekiguchi: A generalization of Okubo type differential equations and flat structures⌗
Date: March 27, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Flat structures are formulated by K. Saito in the course of the study of moduli spaces of isolated singularities. The purpose of this talk is to introduce the notion of flat structures without potentials, formulate one of generalisations of ordinary differential equations of Okubo type to several variables case and give examples of potential vector fields related with algebraic solutions of Painlev'e VI, free divisors arising from 1-parameter deformations of singularities on plane curves and discriminants of complex reflection groups. This is a joint work with M. Kato and T. Mano of University of Ryukyus.
Emre Mengi: Nonlinear Eigenvalue Problems with Specified Eigenvalues⌗
Date: March 25, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Nonlinear eigenvalue problems have drawn substantial interest in the last two decades in numerical analysis. An important concept regarding them is the backward error, that is how much one has to perturb them so that a specified scalar becomes an eigenvalue. Here we consider the following more general question: given an analytic matrix-valued function, where is a nearest one possessing a set of prescribed eigenvalues located? We derive a singular value optimization characterization for such nearest matrix-valued functions with respect to the operator norm induced by the l2 norm. Our derivation benefits from the root canonical form for a nonlinear eigenvalue problem (generalization of the Jordan canonical from), generalized Sylvester operators, as well as tools from complex analysis. This is a joint work with Michael Karow and Daniel Kressner.
Susumu Tanabé: Geometry of oscillating integrals and Dubrovin conjecture⌗
Date: March 18, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
We consider the oscillating integral defined by the polynomial phase function f(x) with non-degenerate singular points. So called « Lefschetz thimble» can be constructed for each singular point of f(x). This integral can be regarded as Laplace transform of the fibre integral associated to the non-singular variety f^{-1}(c). It turns out (F .Pham) that the intersection indices of vanishing cycles of the variety f^{-1}(c) coincide with those of Lefschetz thimbles (regarded as one dimension higher cycles in a relative homology). We show that the elements of the Stokes matrix defined for the oscillating integral calculates exactly the intersection indices mentioned above. As an application we shall discuss the question on the Stokes matrix S for the quantum cohomology of weighted projective space pour P. Namely we shall present a positive answer to the hypothesis proposed by Boris Dubrovin who predicted that the Stokes matrix S coïncide coincides with the Gram matrix of the exceptional collection of coherent sheaves on P. This is a collaboration with Kazushi Ueda.
2014⌗
Haydar GÖRAL: Algebraic Numbers with Small Height Elements⌗
Date: December 24, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The logarithmic height function is a function that measures the complexity of an algebraic number. This is a fundamental notion at the basis of diophantine geometry. In this talk, we study the set of algebraic numbers with small height elements in terms of model theory, in particular we study their combinatorial properties. Then we investigate how this properties are related to some number theoretic results.
Hadia Messaoudene: Comparaison des classes d’opérateurs; de Joël Anderson et la classe des opérateurs finis⌗
Date: December 18, 2014 at 16:00
Location: Galatasaray Üniversitesi FEF 09
Soit H un espace de Hilbert complexe de dimension infinie, L((H) l’algèbre des opérateurs linéaires bornés définis sur H. La dérivation intérieure induite par A est l’opérateur AX-XA; pour tout X de L(H) . On sait que l’ opérateur identité n’ appartient pas à l’ image de la dérivation de l opérateur A . Le but de cet exposé est d’ étudié les classes d’opérateurs où la distance entre l’identité est l’ image d’une dérivation est minimale( classe de Joël ANderson) Où maximale ( classe des opérateurs finis).
Türker Bıyıkoğlu: Entropy, Assortativity, and Hierarchical Structures in Networks⌗
Date: December 17, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy, the spectral radius of the graph’s adjacency matrix, the Randi'c index, and the degree assortativity. We will see that a hierarchical structure; namely, satisfies a breadth-first search ordering with decreasing degrees is a necessary structure for the extremal graphs that maximize these properties.
İrfan ŞİAP: Algebraic Codes and Some Recent Studies⌗
Date: December 03, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
We present the structure of linear codes over some special chain rings by giving a very quick introduction to error correcting codes. These codes have proved to be a good source for DNA codes. We review some recent studies on these directions and we present some new results. We also point out some open problems and new directions.
Emre Alkan: Special values of L-functions and Diophantine approximation type results on the real line⌗
Date: November 26, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will give a survey on the special values of L-functions and especially the Riemann zeta function. We will show how to approximate real numbers by certain combinations of these special values. This is analogous to the Diophantine approximation of Liouville type numbers by rationals. Some open problems will be mentioned.
Piotr Kowalski: Recovering a field from a one-dimensional structure⌗
Date: November 12, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will discuss the model-theoretic notion of interpretability (of one structure in another). For example, the complex field is interpretable in the real field. I will describe my work on algebraically closed fields which are intepretable in ordered fields (joint with Assaf Hasson) and algebraically closed fields which are intepretable in fields with a valuation (joint with Serge Randriambololona).
Michel Lavrauw: Field reduction in finite geometry⌗
Date: November 05, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Based on the well understood concept of subfields in a finite field, the technique called `field reduction’ has proved to be a very powerful tool in finite geometry. In this talk we explain this technique for projective and polar spaces and give some applications.
Olivier Le Gal: O-minimalité et champs de vecteurs⌗
Date: October 30, 2014 at 16:00
Location: Galatasaray Üniversitesi, FEF 09
Dans une première partie, après une introduction rapide à la géométrie o-minimale, on présentera un bref état de l’art des résultats généraux concernant la o-minimalité des trajectoires non oscillantes de champs de vecteurs analytiques. On s’intéressera dans une seconde partie au cas particulier de la dimension trois, où l’on se concentrera sur un résultat de LeGal, Sanz, Speissegger qui montre la o-minimalité des trajectoires non oscillantes appartenant à des pinceaux enlacés.
Deniz Karlı: Stable processes and bounded L^p operators⌗
Date: October 22, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
There is a strong connection between Analysis and Probability Theory. The classical results of Analysis can be obtained by using tools of Martingale Theory, and Brownian motion as the underlying process. Brownian motion is a very specific L'evy process which embraces many ``nice" properties where these properties allows one to reproduce probabilistic alternatives of classical tools. On the other hand, it is possible to study more general L'evy processes with some cost.\ In this talk, we will discuss the question that to what extent we can generalise this process provided that the connection with Analysis is not lost. We will consider some results on bounded linear operators on $L^p(\mathbb{R}^d)$ when the underlying process is taken to be the symmetric stable process which shares some fundamental properties of Brownian motion. We will argue the tools obtained by means of this more general process, and define a new class of harmonic functions to work with. We will also provide a Harnack’s Inequality for this new class of harmonic functions.
Serap Gürer: Topologie algébrique des espaces difféologiques⌗
Date: October 15, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Je vais parler d’études des outils classiques de la topologie algébrique dans le cadre difféologique. Parmi ces outils on se penche particulièrement sur les théories homologiques et cohomologiques généralisées. Un autre objectif est de montrer que les espaces difféologiques offrent un cadre assez naturel afin d’étudier les espaces singuliers. Parmi ces espaces singuliers, on étudie particulièrement les pseudo-variétés contrôlées à la Thom-Mather.
Handan Yıldırım: On Legendrian dualities for the pseudo-spheres in Lorentz - Minkowski space⌗
Date: October 08, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
CIMPA/TÜBİTAK Summer School: Algebraic Geometry & Number Theory⌗
Date: June 02, 2014 at 09:00
Location: Galatasaray University
CIMPA/TÜBİTAK Summer School on Algebraic Geometry and Number Theory. More info: https://math.gsu.edu.tr/2014agnt.html
Ian Morrison: GIT of Hilbert schemes of curves linearized in fixed degree and applications⌗
Date: May 23, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
I will describe briefly constructions of families of projective quotients of Hilbert schemes of curves and their applications both as log-canonical models of the moduli space of stable curves and as moduli spaces in their own right for new classes of curves. Because a degree parameter that could be taken ‘‘sufficiently large’’ in prior constructions must be fixed to go further, classical asymptotic methods for analysing stability are no longer effective. After reviewing this setup, I will outline a new method, joint with David Swinarski, for analysing stability in fixed degree for very special varieties, and conclude by explaining how the method is applied in recent work of Jarod Alper, Maksym Fedorchuk and David Smyth.
Cem Güneri: Algebraic Curves over Finite Fields and Their Rational Points⌗
Date: May 21, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
The aim of the talk is to introduce some of the important facts and problems on curves over finite fields. The number of rational points of such a curve is bounded from above by the Hasse-Weil bound and curves reaching this upper bound are called maximal curves. We will pay particular attention to maximal cuves, especially to Hermitian curve since it is the most interesting maximal curve for various reasons.
Tekin Dereli: Quarks: Who will prove the color confinement conjecture? Mathematicians or Physicists?⌗
Date: May 07, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
One of the seven Millenium Problems announced in 2000 by the Clay Foundation was the “mass gap problem”. This problem is still open and concerns the proof of quark confinement conjecture, crucial for the success of Quantum Chromodynamics (QCD) in sub-nuclear physics. After a quick, broad review of QCD as a quantized field theory, I want to comment on its asymptotic freedom and some consequences of UV-IR duality it implies.
Abdenacer Makhlouf: From Generalized integration to Twisted Rota-Baxter algebras⌗
Date: April 30, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Rota-Baxter operators and Rota-Baxter algebras have appeared in a wide range of areas in pure and applied mathematics (probability, combinatorics, Quantum field theory, algebra ….). It turns out that they are closely related to several algebraic structures. In this talk, I will review the historical developments and some basics. Furthermore, I will describe a twisted version and its relationships with some other algebraic structures.
Ian Morrison: Geometric Invariant Theory and its Applications to Moduli⌗
Date: April 25, 2014 at 09:00
Location: Galatasaray Üniversitesi, FEF 10
Lecture series by Ian Morrison (25 April – 21 May 2014) on Basic Notions of Invariant Theory and Its Applications to Moduli. More info: https://math.gsu.edu.tr/morrison-invariant.html
Patrick Popescu Pampu: The kite of a plane curve singularity⌗
Date: April 18, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk I will present the kite of a plane curve singularity : a bidimensional simplicial complex, which embeds canonically in the space of real semivaluations of the local ring of the ambient surface. It allows to compare all the combinatorial encodings used before in the study of such singularities, and to follow geometrically the computations done with them. This is joint work with Garcia Barroso and Gonzalez Perez.
Finsler Geometry and Applications Conference⌗
Date: April 10, 2014 at 09:00
Location: Galatasaray University
Conference on Finsler Geometry and Applications. More info: https://math.gsu.edu.tr/2014-finsler.html
Ferit Öztürk: Real 3-manifolds can be obtained from real 3-sphere via surgery⌗
Date: April 09, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
A real 3-manifold is a 3-manifold with an orientation preserving involution. 3-sphere has a unique real structure with nonempty fixed point set up to equivariant isotopy. It is well-known that every 3-manifold can be obtained from the 3-sphere via +1 and -1 surgeries along a finite collection of knots. In this talk we will prove that any real 3-manifold can be obtained from the real 3-sphere via surgery along a finite “recursively invariant” collection of knots.
Sevgi Perek: İş Yaşamında Yönetici ve Yaşam Koçluğu⌗
Date: March 26, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Japanese-Turkish Joint Geometry Conference II⌗
Date: March 19, 2014 at 09:00
Location: Galatasaray University
Second Japanese-Turkish Joint Geometry Conference. More info: https://math.gsu.edu.tr/2014-geometry.html
Serkan Sütlü: Characteristic classes of foliations via SAYD-twisted cocycles⌗
Date: March 12, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk we present our construction of a characteristic map, using a “SAYD-twisted” cyclic cocycle, by which we transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of a certain noncommutative algebra. We carry out the explicit computation in codimensions 1 and 2. In codimension 1, we show how our result matches with the (only explicit) computation done by Connes-Moscovici, and in codimension 2 we present the transverse fundamental class, the Godbillon-Vey class, and the other four residual classes as cyclic cocycles. This is a joint work with B. Rangipour.
Aybike Özer: Dualities in string theory⌗
Date: March 05, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This talk is comprised of two parts: In the first part, which will be mostly non-technical, I will give a general overview of various duality symmetries in string theory. Then I will explain (part of) our work, where we establish an S-duality relation between the two massive theories obtained from twisted compactifcations of heterotic and IIA string theories down to four dimensions.
2013⌗
Hatice Boylan: Finite dimensional representations of SL_2 over maximal order in a number field⌗
Date: December 25, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
In various applications of automorphic forms it becomes crucial to know the finite dimensional representations of SL_(2,O), where O is a maximal order in a number field. There are amazingly open questions concerning these representations. But recently there has been some progress. In particular, we determined all linear characters of SL(2,O) and we applied the general theory of Weil representations of locally compact abelian groups invented by Weil to generate interesting family of representations of SL(2,O) which possibly contain all finite dimensional representations of SL(2,O) of finite image."
Ayhan Gunaydin: Uniform Versions of the Mordell-Lang Conjecture for Multiplicative Groups⌗
Date: December 18, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The Mordell-Lang Conjecture (MLC) concerns finitely generated subgroups of abelian varieties, however, there are analogous statements in the “non-compact” case: namely the case of the (cartesian powers of) multiplicative group, G_m. (Sometimes, MLC is formulated for semi-abelian varieties to include this case.) In very heuristic terms, in the multiplicative group case, MLC says “the addition doesn’t give new information about finitely generated multiplicative groups of fields.” (This will be made clear in this talk.) We isolate the conlusion of MLC as an abstract property for subgroups of G_m. It turns out that many groups other than finitely generated ones have this property. Moreover, some of them satisfy a uniform version of it. Vaguely, this corresponds to the function field field case of MLC. In this talk, after making everything above more accurate, we prove that certain finitely generated groups have this “uniform” Mordell-Lang Property.
M. Ali Akinlar: On the numerical solution and control of dynamics of some fractional differential equations⌗
Date: December 11, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
This talk separated into three major parts: First overview of fractional calculus, secondly approximate and analytical solutions of some fractional partial differential equations and third analysis of dynamical features of some particular fractional dynamical systems.
Kazim Büyükboduk: An asymptotic Birch and Swinnerton-Dyer Conjecture⌗
Date: December 04, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The conjecture of Birch and Swinnerton-Dyer (BSD) is one of the Clay Millennium problems that links the arithmetic invariants of an elliptic curve to its analytic invariants. Most of this talk will be devoted to explaining the contents of this conjecture and stating its asymptotic variant. As time permits, I will sketch a proof of the asymptotic BSD for CM elliptic curves, which relies on the Iwasawa theoretic study of the Kato-Beilinson elements and the reciprocity law that relates them to relevant L-functions.
Nilay Duruk Mutlubaş: On periodic solutions of a model equation for surface waves of moderate amplitude in shallow water⌗
Date: November 27, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
In this talk, we study the local well-posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water. We use an approach due to Kato which is based on semigroup theory for quasi-linear equations. We also show that singularities for the model equation can occur only in the form of wave breaking, in particular surging breakers.
Japanese-Turkish Joint Geometry Meeting⌗
Date: November 21, 2013 at 09:00
Location: Galatasaray University
Japanese-Turkish Joint Geometry Meeting. More info: https://math.gsu.edu.tr/2013jpn-tr.html
Mutsuo Oka: Mixed functions of strongly polar weighted homogeneous face type⌗
Date: November 20, 2013 at 16:00
Location: IMBM
Let $f(\bfz,\bar\bfz)$ be a mixed polynomial with strongly non-degenerate face functions. We consider a canonical toric modification $\pi:,X\to \BC^n$ and a polar modification $\pi_{\BR}:Y\to X$. We will show that the toric modification resolves topologically the singularity of $V$ and the zeta function of the Milnor fibration of $f$ is described by a formula of a Varchenko type.
William Gillam: Logarithmic structures in algebraic and differential geometry⌗
Date: November 13, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Logarithmic structures were introduced into algebraic geometry by Kato, Fontaine, and Illusie as a generalization of the toric embeddings studied earlier by Mumford and others. Roughly speaking, the theory furnishes a category where the nicest object is a smooth variety equipped with a normal crossings divisor. We will survey some applications of this machinery in the construction and study of various moduli spaces and in the context of degeneration formulas in Gromov-Witten and Donaldson-Thomas theory. We will also discuss a version of this theory in differential geometry—where manifolds with corners are the nicest objects—and explain how this is related to the algebro-geometric side of the theory.
Serge Randriambololona: Un survol de l’o-minimalité et de quelques unes de ses applications⌗
Date: October 23, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
La théorie des structures o-minimales est une généralisation de la géométrie semi-algébrique (l’étude des ensembles de $\mathbb R^n$ définis par un système fini de lieu d’annulation et de lieu de positivité de polynômes), apparue dans le milieu des années 80 dans un papier de L. van den Dries et formalisé plus tard par Pillay et Steinhorn. Elle propose une approche axiomatique de ce que peut-être une géométrie “modérée” (comme proposé par Grothendieck dans son “esquisse d’un programme”), présente de nombreux exemples naturels (une des activités importante dans le domaine constitue à établir si une théorie donnée est o-minimale ou non) et présente une souplesse qui lui permet d’établir le bon comportement de nombreux objets géométriques naturels. Je préciserai la définition d’une structure o-minimal, expliquerai les principaux théorèmes qui font qu’on la considère comme un cadre “modéré”, donnerai des exemples importants de structures o-minimales et présenterai certain de ses succès récents en théorie des nombres.
Asli Deniz: Introduction to Holomorphic Dynamics: An Extension of Holomorphic Motion⌗
Date: October 09, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The talk consists of four sections: First, we give a short introduction to the field of holomorphic dynamics. In the second section, we introduce a specific one parameter family of transcendental entire functions. In the third part, we give a new concept termed holomorphic explosion, which we derived from holomorphic motion. The last section is devoted to an application of holomorphic explosion to the transcendental entire family in consideration.
Şükrü Yalçınkaya: Black Box Groups⌗
Date: September 25, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Black box groups are introduced as an idealised setting for randomised al- gorithms for solving permutation and matrix group problems in computational group theory. A black box group G is a finite group whose elements are encoded as 0-1 strings of uniform length and the group operations are performed by an oracle (‘black box’). Given strings representing g, h in G, the black box can compute the strings representing gh, g^{-1} and decide whether g = h. In this context, a natural task is to find a probabilistic algorithm which determines the isomorphism type of a group within given (arbitrarily small) probability of error. More desirable algorithms, called constructive recognition algorithms, are the ones producing an isomorphism between a black box copy of a finite group and its natural copy. A simple observation on the recognition algorithms in black box group theory is that procedures are based on checking whether some first order formulae satisfied by the given black box group. I will focus on this observation and discuss constructive recognition of black box groups of Lie type. Along the way, I will explain how we define a standard Frobenius automorphism in a black box group isomorphic to (P)SL(2, q) and construct (or interpret) of a black box field in black box groups using only black box group operations. If time permits, I will talk about the interpretation of inverse transpose map and graph automorphisms, and the corresponding constructions in the black box groups of Lie type. This is a joint work with Alexandre Borovik.
MSGSU-GSU Toric and Tropical Geometry Meetings⌗
Date: September 15, 2013 at 09:00
Location: Galatasaray University / Mimar Sinan Güzel Sanatlar Üniversitesi
Recurring weekly meetings on Toric and Tropical Geometry (2013). More info: https://istanbulttgmeetings.wordpress.com
Evrim Hilal Erdamar (Sermaye Piyasası Kurulu): Comovement between stock and bond return in Turkey.⌗
Date: May 22, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
We try to determine the relation between stock returns and changes in interest rates and attribute this relation to one of two competing hypotheses: similarity in valuation methods implying a negative relation and need for a portfolio reallocation implying a positive correlation. We find a negative correlation (-0.33), hence support the first hypothesis. However, this correlation has weakened in the period after the subprime crisis of 2007 (-0.37 vs. -0.28). Interestingly, sharp decreases in interest rates are associated with high positive correlations while sharp increases are associated with high negative correlations. This reveals an asymmetry in the relation between stock and bond returns. We also find that some sectorial indices have different sensitivities to interest rate changes.
Athanase Papadopoulos: Structure métrique de l’espace de Teichmüller⌗
Date: May 15, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Gönenç Onay: Valued Difference Fields⌗
Date: May 08, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
To a valued field one can canonically associate its residue field and value group. It is natural to ask the following question: if two valued fields have “similar” valued groups and “similar” residue fields how much are they similar as valued fields? For example, (Q_p,v_p) and (F_p((t)), v_t) have the same residue field (F_p) same and the value group (Z) and Ax-Kochen and Ershov theorem establish a “tight” similarity between this two fields that answers a conjecture of Artin. I will discuss the analogous situation where the valued fields in question are respectively equipped by distinguished automorphisms.
Evelia Garcia Barroso (Universidad de La Laguna-Tenerife): A criterion of irreducibility for complex series in two variables.⌗
Date: April 24, 2013 at 15:00
Location: Galatasaray University, FEF 10
We give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction.
Evelia Garcia Barroso (Universidad de La Laguna-Tenerife): Resolution of singularities of plane curves I-II⌗
Date: April 22, 2013 at 14:00
Location: Galatasaray University, FEF 9
(Abstract not available in text)
Burak Özbağcı: Exotic Stein fillings with arbitrary fundamental group⌗
Date: April 03, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
For any finitely presentable group G, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings whose fundamental group is isomorphic to G. Along the way, we also provide a new construction of a Lefschetz fibration over the 2-sphere whose total space has fundamental group G, using Luttinger surgery. (This is a joint work with Anar Akhmedov)
Masaaki Yoshida (Université Kyushu): 6 planes in the space⌗
Date: March 22, 2013 at 10:00
Location: Galatasaray Üniversitesi FEF 10
I will give lectures about 6 planes in the space (joint work with B. Morin): Real projective line, plane, space: definition and intuitive understanding. projective transformations. Point arrangements on the line, line arrangements on the plane, plane arrangements in the space. Six planes in the space: observation and recognition which can be very elementary.
Masaaki Yoshida: Schwarz maps for hypergeometric functions⌗
Date: March 20, 2013 at 10:30
Location: Galatasaray Üniversitesi FEF 8 - FEF 10
Review of the hypergeometric function, equation and the Schwarz map. Few comments on several high-dimensional generalizations. After these, I introduce the hyperbolic Schwarz map, whose image is a surface in the 3-dimensional hyperbolic space
İstanbul Number Theory Meetings II⌗
Date: March 16, 2013 at 09:00
Location: Galatasaray University (Barlas Tolan)
Meeting featuring talks on o-minimal structures and number theory, including ‘A Fast Introduction to O-minimality’ and applications of the Pila-Wilkie counting theorem (Manin-Mumford conjecture). More info: https://math.gsu.edu.tr/2013intm-8.html
Jean-Paul Brasselet (CIRM, Marseille): Orbits divisors on toric varieties.⌗
Date: March 13, 2013 at 13:30
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Jean-Paul Brasselet (CIRM, Marseille): Projective Toric Varieties.⌗
Date: March 11, 2013 at 14:00
Location: Galatasaray Üniversitesi FEF 9
(Abstract not available in text)
Refik Arkut: Internet, Karmaşıklık, MOOC ve Gelecekte Eğitim.⌗
Date: February 27, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Bu seminerde konuşmacı kendi kişisel deneyimlerini, Internet’in başlangıç noktasından başlayarak anlatacak ve karmaşıklık kuramı ile ilk tanışmasının verdiği merakla, öğrenme dürtüsünün kendisini getirdiği MOOC (Massively On-line Open Course)’taki son ‘öğrencilik’ macerasına değinecektir. Henüz emekleme çağındaki Internet’in bize gelecekte neler sunabileceği konusunuda öngörülerini ‘Gelecekte Eğitim’ örneği ile tartışacaktır. Seminerde SFI (Santa Fe Institute) düzenlenen (on-line) ‘Introduction to Complexity’ dersinden bazı örnekler sunulacaktır.
İstanbul Number Theory Meetings I⌗
Date: February 16, 2013 at 09:00
Location: IMBM, Istanbul
Meeting featuring four speakers from Istanbul universities discussing automated theorem proving, subgroups of infinite dihedral groups, binary quadratic forms, and Thompson’s groups. More info: https://math.gsu.edu.tr/2013intm.html
Thomas Hudson: An extension of Schubert polynomials for connected K-theory using algebraic cobordism.⌗
Date: January 10, 2013 at 11:00
Location: Galatasaray Üniversitesi FEF 8
Given a suitably generic morphism of vector bundles over a smooth scheme X, the Chow ring fundamental classes of the degeneracy loci can be expressed by means of the double Schubert polynomials. This result has an exact analogue in K^0(X), the Grothendieck ring of algebraic vector bundles over X, provided one replaces the double Schubert polynomials with the double Grothendieck polynomials. In this talk I will illustrate the common framework existing behind this two results and how it can be transported to algebraic cobordism, the universal oriented cohomology theory. I will also explain how this approach allows, in the universal case of a full flag bundle, to extend the result to connected K-theory, a cohomology theory that dominates both CH and K^0, leading to the definition of a family of polynomials generalizing both Schubert and Grothendieck polynomials.
2012⌗
Alp Bassa: Elliptic Curves, Drinfeld Modules and Curves over Finite Fields⌗
Date: December 26, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk I will start by introducing Elliptic Curves and their characteristic p analogues, Drinfeld Modules. I will talk about modular curves and varieties, which parametrize these objects and show how they can be used in the construction of curves over finite fields with many rational points.
Kamel Haouam: Qu’est-ce que la didactique des Mathématiques?⌗
Date: December 19, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
La didactique des mathématiques est une nouvelle science âgée de trente ans ou un peu plus, elle s’intéresse à l’étude de la transmission du savoir mathématique, en conséquence plusieurs questions se constituent à savoir: - comment le savoir s’est-il construit. - quel est le rôle de l’enseignant vis à vis de ce savoir. - suffit-il seulement de remplir les têtes vides des apprenants? On se rend compte alors qu’on est convaincu que ceci ne se réduit seulement pas à l’acquisition des contenus secs des mathématiques, c’est à partir de là que commence la didactique.
İrem Portakal: Quivers, polytopes and toric varieties⌗
Date: December 12, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
A quiver is simply an oriented graph without oriented cycles. They are frequently used to represent some of the important results in many areas of mathematics. It has shown that every quiver leads to a reflexive polytope the one we call a flow polytope. I will present a method to determine a finite list of quivers defining all d dimensional flow polytopes up to isomorphism. Also, I will describe how we can associate these purely combinatorial objects to toric varieties. One can ask if we can “understand” toric varieties by looking at its associated quiver. It still remains as an open question if one can find a criterion for smoothness of associated toric variety in terms of quiver.
Frédéric Chapoton: Combinatoire des triangulations⌗
Date: November 30, 2012 at 13:00
Location: Galatasaray Üniversitesi FEF 10
Je vais présenter plusieurs objets combinatoires remarquables (les frises de nombres, les triangulations etc.) et parler de relations parfois surprenantes entre ces différents objets. Les nombres de Catalan permettent de compter tous ces objets.
Frédéric Chapoton: Tree-indexed series⌗
Date: November 28, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Rooted trees have a rich algebraic structure, and they have been used in various domains of mathematics, including numerical analysis and renormalisation. I will present some of these algebraic structures, in particular on the vector space of tree-indexed series, which can be thought of as an analogue of formal power series. I will also describe some examples of interesting tree-indexed series.
Müge Taşkın: Tower tableaux⌗
Date: November 14, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
It is well known that any permutation w in the symmetric group Sn can be represented as the product of some finite adjacent transpositions si = (i; i + 1) where the index i runs from 1 to n - 1. Among all such representations the ones which uses the minimum number of generators are called reduced representations for w. The notion of reduced words has been catching high attention, because of their appearances in many areas that algebraic combinatorics interferes. In this talk, we introduce a new combinatorial object ”tower tableaux" together with the ”sliding algorithm" which appears as an important tool for studying reduced words in many aspects.
Vasile Berinde: Some numerical aspects of fixed point iterative methods for solving nonlinear optimization problems⌗
Date: November 05, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Stepan Orevkov: Real algebraic and real pseudoholomorphic curves⌗
Date: October 31, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Real pseudoholomorphic curves in real algebraic surfaces (in projective plane, for example) have many properties in common with real algebraic curves. If a given configuration of ovals on $RP^2$ is realizable as the set of real points of a real pseudoholomorphic curves, usually it is rather difficult to prove that it is algebraically unrealizable.In my talk,I will discuss some cases when it is nevertheless possible.
İstanbul Workshop on Teichmüller Theory⌗
Date: October 11, 2012 at 09:00
Location: Istanbul
İstanbul Workshop on Teichmüller Theory. More info: https://math.gsu.edu.tr/2012iwtt.html
İstanbul Workshop on Fixed Point Theory and Applications⌗
Date: October 11, 2012 at 09:00
Location: Galatasaray University
International workshop (11-14 October 2012) on fixed point theory with emphasis on applications in natural sciences, economics, finance, computing, and engineering. More info: https://math.gsu.edu.tr/2012iwfpta.html
ICTB Workshop on Recent Trends in Algebraic Number Theory⌗
Date: June 15, 2012 at 09:00
Location: Galatasaray University
ICTB Workshop on Recent Trends in Algebraic Number Theory (June 2012). Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
CIMPA Meeting on Regional Cooperation⌗
Date: June 15, 2012 at 09:00
Location: Galatasaray University
CIMPA meeting on regional cooperation (June 2012). Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
Ayşe Berkman: Characterizing Groups of Finite Morley Rank via Their Actions⌗
Date: May 29, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
After explaining some model theoretic concepts such as Morley rank, I shall state some characterization results of certain linear groups in the finite Morley rank context. Then I shall discuss how these results can be used in understanding generically sharp transitive actions. The talk will be accessible to graduate students.
Emel Bilgin (Univ. Essen): Classes of hypersurfaces of low degree in the Grothendick ring of varieties K_0(Var_k).⌗
Date: May 25, 2012 at 14:30
Location: Galatasaray Üniversitesi FEF9
(Abstract not available in text)
Murat Turhan (Yıldız Teknik Üniversitesi): Hirota type discretization⌗
Date: May 15, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 10
The integrable discretizations of the problems in rigid body dynamics are a vast undeveloped area of study. Certainly, the most famous ones are the three integrable cases of the rotation of a heavy rigid body around a fixed point in a homogeneous gravity field, named after Euler, Lagrange and Kowalevski. Recent studies for the integrable discrete systems show us the conspicuous relationships in unrelated areas of research such as numerical algorithms, discrete geometry, cellular automaton, quantum integrable systems and algebraic geometry tools. One of these studies, Bobenko and Suris, use Poisson construction of discretizations which gives implicit equations of motion. In this talk, we give a very different discretization method, called Hirota type discretization, using the bilinear transformation method and obtain explicit equations of motion. We give Hirota discretization of the motion of a rigid body with a fixed center of mass named Euler Top.
Nicolas Vayatis (ENS, Cachan): Statistical Learning Theory: a playground for the mathematics of prediction.⌗
Date: May 10, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 8
Les mathématiques de la prévision ont longtemps privilégié la notion de régularité locale des modèles (conditions d’existence de solutions dans les EDP, propriété des modèles statistiques garantissant la convergence des estimateurs paramétriques, etc). La théorie de l’apprentissage statistique, quant à elle, propose des concepts de nature combinatoire (complexités de Vapnik-Chervonenkis) ou géométriques (complexités de Rademacher) comme garants de la qualité des modèles à vocation prédictive. La révolution est de taille puisque cette approche récente permet d’aborder de front les questions d’inférence relatives à l’exploitation de données en grande dimension. Elle nourrit également de questionnements une communauté croissante de chercheurs confrontant informaticiens et mathématiciens issus de spécialités diverses (probabilités, statistique mathématique, géométrie convexe, optimisation) autour d’une thématique commune. L’exposé se fera l’écho des avancées récentes au sein de cette théorie aux retombées spectaculaires dans la technologie moderne.
Mihai Tibar (Univ. Lille 1, France): Betti numbers of polynomials⌗
Date: April 24, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
We explain how to initiate a classification of polynomials f from C^n to C of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may have at most one line singularity of Morse transversal type. Our method uses deformations into particular pencils with non-isolated singularities. This is a joint work with Dirk Siersma.
Haluk Şengün (University of Warwick): Cohomology of Bianchi Groups⌗
Date: April 17, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They arise naturally in the study of hyperbolic 3-manifolds and of certain generalizations of the classical modular forms (called Bianchi modular forms) for which they assume the role of the classical modular group SL(2,Z). In this latter sense, the study of Bianchi groups is fundamental for developing Langlands’ programme for GL(2) beyond totally real fields. The overall goal of this talk is to give the audience an overview of some of the fundamental problems in the arithmetic aspects of the theory of Bianchi groups. After giving the necessary background, I will start with a discussion of the problem of understanding the behavior of the dimensions of the cohomology of Bianchi groups and their congruence subgroups. Next, I will focus on the amount of the torsion that one encounters in the cohomology . Finally, I will discuss the arithmetic significance of these torsion classes.
Vincent Labatut (Université de Galatasaray): Complex Networks Analysis⌗
Date: April 10, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Networks science constitutes a very dynamic field in current research. It can be historically considered as the intersection of three preexisting domains: graph theory, complex systems analysis and data mining. Due to the great flexibility of graphs used as a modeling tool, the theoretical results obtained in network science are used in numerous applied sciences, including biology, physics, computer science, economy, human sciences, etc. In this presentation, we will first briefly describe the emergence of this relatively new field, and present its goals. We will then introduce its main concepts, and the most important results obtained in this field. We will also use a few real-world examples to illustrate what these results practically mean and show their scope. Finally, we will present the open questions currently at the center of the attention in this field.
Mark Spivakovsky (Université de Toulouse): Introduction to the problem of resolution of singularities⌗
Date: April 03, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
The aim of the talk is to give an introduction to the problem of resolution of singularities in characteristic zero and in positive characteristic (all notions required to state the problem will be defined during the talk). If time permits, we shall discuss the local version of the problem, so called “local uniformization with respect to a valuation”.
Jiro Sekiguchi (Tokyo University of Agriculture and Technology): Free Divisors and Painlevé Equations after M. Kato⌗
Date: March 20, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
First of all, I will explain the definition of free divisors and that of systems of uniformization equations with singularities along such hypersurfaces which are examples of holonomic systems. These two notions are formulated by K. Saito around 1970’s. Then I restrict my attention to the case of hypersurfaces of an affine three dimensional space. I will show some examples of free divisors in this case and uniformization equations. It turns out that the systems of uniformization equations are closely related with Painlevé equation and its algebraic solutions. Typical examples of free divisors are hypersurface defined by the discriminant of real and complex reflection groups. Recently M. Kato (Univ. of Ryukyus) clarified the relationship between systems of uniformization equations with singularities along the discriminant sets of reflection groups of rank three and algebraic solutions of Painlevé equation. In my talk I will take a survey of free divisors, uniformization equations, and discuss topics related with the results of M. Kato.
Richard Gonzales (Galatasaray University): Standard group embeddings and divided differences operators⌗
Date: March 13, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Briefly speaking, a standard group embedding is a normal projective compactification of a reductive group. They can all be obtained as certain projectivizations of reductive monoids. A complete combinatorial description of the equivariant cohomology of rationally smooth embeddings (a subclass that includes smooth and certain singular varieties), has been obtained in previous work by the author. An interesting open problem is to find an explicit set of polynomial generators for the various cohomology rings thus obtained. In this introductory talk, I will provide a survey of these topics and show how Newton’s divided difference operators (and Schubert calculus) could be effectively used to solve the above-mentioned problem. This is joint work with K. Aker and Ö. Öztürk.
Dr. Ayşe Altıntaş (Yıldız Teknik Üniversitesi): Examples of finitely determined map-germs⌗
Date: February 28, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 10
The main focus of this talk will be finitely determinacy of multi valued holomorphic map-germs with respect to the Right-Left equivalence. By J. Mather’s results, finite determinacy can be characterised geometrically. An important tool for studying the geometry of maps is the notion of multiple point spaces. The k-th multiple point space of a finite map between topological spaces is the closure of the set of k-tuple points having the same image under the map and distinct components. In this talk, I shall discuss how to get algebraic criteria for finite determinacy of map-germs of any corank from 3-space to 4-space using multiple point spaces and demonstrate it with examples.
2011⌗
Bernard Teissier (Institut Mathématique de Jussieu, Equipe Géométrie et Dynamique): On the Lojasiewicz exponent⌗
Date: December 29, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
The Lojasiewicz exponent measures the relative rates of vanishing of two real or complex-analytic, or subanalytic, functions which vanish on the same set. I will survey some variations on this idea in commutative algebra, including if time permits a recent result of Moret-Bailly on the Artin-Greenberg approximation theorem.
Cemsinan Deliduman (Mimar Sinan Güzel Sanat Üniversitesi): Entanglement Swapping Model of DNA Replication⌗
Date: December 22, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
Molecular biology explains function of molecules by their geometrical and electronical structures which are mainly determined by utilization of quantum effects in chemistry. However,further quantum effects are not thought to play any significant role in the essential processes of life. On the contrary, consideration of quantum circuits/protocols and organic molecules as software and hardware of living systems that are co-optimized during evolution, may be useful to pass over the dfficulties raised by biochemical complexity and to understand the physics of life. In this talk, I will describe a quantum mechanical model of DNA replication with a reliable qubit representation of the nucleotides. In the model: 1) molecular recognition of a nucleotide is assumed to trigger an intrabase entanglement corresponding to a superposition of different tautomer forms and 2) pairing of complementary nucleotides is described by swapping intrabase entanglements with interbase entanglements. I will give some examples of quantum circuits/protocols to be used to obtain intrabase and interbase entanglements. Lastly, possible computational and experimental verification methods of the model will be discussed.
Arnaldo Garcia (IMPA at Rio de Janeiro, Sabancı Üniversitesi): Asymptotics on codes and on curves over finite fields⌗
Date: December 08, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
The famous bound of Hasse-Weil for the number of rational points on curves over finite fields (equivalent to the Riemann Hypothesis in this context) was shown by Ihara to be weaker as the genus of the curve grows. For a finite field with q elements, Ihara then introduced the quantity A(q) that controls the asymptotic behaviour of the number of rational points as the genus goes to infinity.To deal with A(q) one is led to consider infinite towers of algebraic curves and to study their limits for the ratios of (number of rational points) / (genus). We are going to motivate this interesting mathematical subject by its connection to the asymptotics in Coding Theory, which is a result due to Tsfasman-Vladut-Zink based on a construction of Goppa of linear codes from algebraic curves over finite fields.
Geometry and Arithmetic around Teichmüller Theory Conference⌗
Date: November 15, 2011 at 09:00
Location: Galatasaray University
Conference on Geometry and Arithmetic around Teichmüller Theory. More info: https://math.gsu.edu.tr/2011gatt.html
Ayberk Zeytin (Galatasaray University): Polygonal decompositions of the sphere and ball quotients⌗
Date: November 03, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
After a short introduction to the subject, we will give classification of sphere quadrangulations satisfying a condition of non-negative curvature, following Thurston’s classification of sphere triangulations under the same condition. If time permits, we will discuss some arithmetic applications of the classification, and its relations to Picard-Terada-Deligne-Mostow theory. (joint with M.Uludag.)
Johannes HUEBSCHMANN (Université des sciences et technologies de Lille): Singular Poisson-Kähler geometry of stratified Kähler spaces⌗
Date: May 09, 2011 at 15:30
Location: salle P20
(Abstract not available in text)
Eugene HA (Galatasaray Üniversitesi): Galois Theory from Galois’ Perspective⌗
Date: May 04, 2011 at 16:00
Location: salle FEF 8 (mercredi) et FEF 1 (jeudi)
These lectures will cover the main theorem of the Galois theory of fields following closely the original approach of Galois. We will see how Galois theory proves the nonexistence of a general algebraic formula for the roots of rational-coefficient polynomials of degree 5 or more. We shall also illustrate the general theory in the special case of cyclotomic fields and of finite fields.
Müge KANUNI (Boğaziçi Üniversitesi): Discrete Structures in Algebra⌗
Date: April 25, 2011 at 15:00
Location: salle P20
Path Algebras, Leavitt Path Algebras and Incidence Algebras are algebras defined on discrete structures. We will describe these different structures and give a brief overview of their history.
Meral TOSUN (Université Galatasaray): Good slices for simple elliptic singularities⌗
Date: April 04, 2011 at 15:00
Location: salle P20
We will first present the relation between singularities of complex surfaces and Lie algebras. Then we will show how to generalize the Slodowy slices to simple elliptic singularities.
Fonktörsellik ve Eşleşme (Functoriality Short Course)⌗
Date: March 30, 2011 at 09:00
Location: Galatasaray Üniversitesi
Intensive short course (30 March – 27 April 2011) featuring Robert Langlands and other mathematicians on functoriality, reciprocity principles, L-functions, trace formulas, and geometric approaches. More info: https://math.gsu.edu.tr/fonktorsellik.html
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): Espaces métriques généralisés 2⌗
Date: March 24, 2011 at 09:00
Location: salle FEF 5
(Abstract not available in text)
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): Espaces métriques généralisés 1⌗
Date: March 23, 2011 at 16:00
Location: salle FEF 10
(Abstract not available in text)
Jiro SEKIGUCHI (Tokyo University of Agriculture and Technology): A Schwarz map of Appell’s F_2 whose monodoromy group is related to the reflection group of type D_4⌗
Date: March 21, 2011 at 16:00
Location: salle FEF 7
The system of differential equations for Appell’s hypergeometric function F_2(a,b,b’,c,c’;x,y) has four fundamental solutions. Let u_1,u_2,u_3,u_4 be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y)) is a hypersurface S of the 3-dimensional projective space {\bf P}$. Then S is defined by P(u_1,u_2,u_3,u_4)=0 for a polynomial P(t_1,t_2,t_3,t_4). It is M. Kato (Univ. Ryukyus) who determined the parameter a,b,b’,c,c’ such that the monodromy group of the system for F_2(a,b,b’,c,c’;x,y) is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group G of rank four by an abelian group. In this talk, we treat the system for F_2(a,b,b’,c,c’;x,y) with (a,b,b’,c,c’)=(1/2,1/6,-1/6,1/3,2/3. In this case, the monodromy group is the semidirect group of G by Z/3Z, where G is the reflection group of type D_4. The polynomial P(t_1,t_2,t_3,t_4) in this case is of degree four. There are 16 ordinary singular points in the hypersurface S. In the rest of my talk, I explain the background of the study.
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): La géométrie de Finsler⌗
Date: March 21, 2011 at 15:00
Location: salle FEF 7
(Abstract not available in text)
Eric SOCCORSI (centre de physique théorique, Marseille): Résolution des équations différentielles par la méthode des élements finis⌗
Date: March 16, 2011 at 15:00
Location: salle FEF 9
J’expliquerai comment on résout “numériquement” une EDP en prenant pour simplifier un exemple d’EDO.
Eric SOCCORSI (centre de physique théorique, Marseille): Lipschitz stability in an inverse problem for non autonomous magnetic Schrödinger equations⌗
Date: March 14, 2011 at 16:00
Location: salle FEF 7
We consider the inverse problem of determining the time dependent magnetic field of the Schrödinger equation in a bounded open subset of R^n, n>=1, from a finite number of Neumann data, when the boundary measurement is taken on an appropriate open subset of the boundary. We prove the Lispchitz stability of the magnetic potential in the Coulomb gauge class by n times changing initial value suitably.
Oleg BELEGRADEK (İstanbul Bilgi Üniversitesi): How similar can non-isomorphic algebraic structures be?⌗
Date: March 14, 2011 at 15:00
Location: salle FEF 7
In this talk (oriented to a general mathematical audience not necessarily familiar with model theory) I will discuss the notion of elementary equivalence, one of the basic notions of model theory, illustrating it with various algebraic examples, both classical and more recent. In particular, some author’s results on model-theoretic properties of unitriangular groups will be discussed.
Jawad SNOUSSI (Universidad Nacional Autónoma de México): Modifiactions des singularités⌗
Date: March 09, 2011 at 15:00
Location: salle FEF 10
Nous expliquerons les concepts d’éclatement, de normalisation, de modification de Nash et leur relations avec la résolution des singularités
Jawad SNOUSSI (Universidad Nacional Autónoma de México): Equisingularity in complex surfaces⌗
Date: March 07, 2011 at 15:00
Location: salle FEF 4
We explain the equivalence for complex surfaces between Whitney regularity and Zariski equisingularity criterion. We will give some applications such as the fact that any surface Whitney regular along its singular locus has a smooth normalisation.
Eugene HA (Université Galatasaray & Fields Institute, Toronto): The problem of cohomology for an Arakelov divisor⌗
Date: February 28, 2011 at 15:00
Location: salle P 23
We shall discuss Tate’s Riemann-Roch theorem for number fields and the peculiar nature that it implies for the cohomology of an Arakelov divisor (that is, a divisor for the spectrum of a number field formally completed at archimedean infinity).
Gülay KAYA (Université Galatasaray): The Groebner fan of a polynomial ideal⌗
Date: January 07, 2011 at 15:00
Location: salle FEF 1
(Abstract not available in text)
2010⌗
Muhammed ULUDAĞ (Université Galatasaray): Hypergeometric Galois Actions⌗
Date: December 20, 2010 at 15:00
Location: salle FEF 9
(Abstract not available in text)
Cédric MILLIET (Université Galatasaray): Quelques mots de théorie des modèles⌗
Date: December 06, 2010 at 15:00
Location: salle FEF 9
Le but de l’exposé est de faire voir un peu de théorie des modèles. J’ai choisi de présenter un théorème de Macintyre (de 1971) disant qu’un corps omega-stable est soit fini, soit algébriquement clos. Après avoir dit ce qu’est une théorie, ou un modèle, et énoncé quelques questions typiques que se posent habituellement les logiciens, je rappelerai deux invariants des espaces topologiques compacts dénombrables qui permettent de les classifier à homéomorphisme près, avant de donner une preuve du théorème de Macintyre, allégée grâce à des arguments de Poizat. L’exposé devrait être accessible à tous.
Susumu TANABE (Université Galatasaray): Invariants of hypergeometric groups for Calabi–Yau complete intersections in weighted projective spaces⌗
Date: November 24, 2010 at 17:15
Location: salle FEF 9
Let Y be a smooth Calabi–Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the mirror manifold of Y in the sense of Batyrev and Borisov is one-dimensional and spanned by the Gram matrix of a classical generator of the derived category of coherent sheaves on Y with respect to the Euler form. This is a confirmation of an expected consequence of the homological mirror symmetry conjecture by Kontsevitch.
Xavier BRESSAUD (Institut de Mathématiques de Toulouse): Introduction à la dynamique symbolique. (2/2)⌗
Date: November 05, 2010 at 10:00
Location: salle P 19
(Abstract not available in text)
Xavier BRESSAUD (Institut de Mathématiques de Toulouse): Introduction à la dynamique symbolique. (1/2)⌗
Date: November 04, 2010 at 10:00
Location: salle FEF 9
(Abstract not available in text)
Hervé GAUSSIER (Institut Joseph Fourier, Grenoble): Pseudoholomorphic curves and applications⌗
Date: October 27, 2010 at 16:00
Location: salle FEF 10
Pseudoholomorphic curves are important objects by their role in different subjects such as symplectic or contact geometry. I will present recent results on the study of almost complex manifolds, concerning the (non)existence of pseudoholomorphic curves and more generally of pseudoholomorphic maps.
Hervé GAUSSIER (Institut Joseph Fourier, Grenoble): Géométrie et calcul infinitésimal. Séminaire introductif à destination des étudiants⌗
Date: October 26, 2010 at 15:00
Location: salle FEF 1
J’essaierai de montrer les liens entre la géométrie classique, notamment la construction à la règle et au compas, et les premières études sur le calcul différentiel. Je montrerai aussi l’évolution de la géométrie euclidienne vers d’autres géométries.
CIMPA/TÜBİTAK Summer School: Commutative Algebra & Applications⌗
Date: September 12, 2010 at 09:00
Location: Galatasaray University
CIMPA/TÜBİTAK Summer School on Commutative Algebra and Applications. More info: https://math.gsu.edu.tr/2010/
2009⌗
GTEM/TÜBİTAK Summer School: Geometry & Arithmetic around Galois Theory⌗
Date: June 08, 2009 at 09:00
Location: Galatasaray University
GTEM/TÜBİTAK Summer School on Geometry and Arithmetic around Galois Theory. More info: https://math.gsu.edu.tr/GAGT/
2008⌗
GTEM/TÜBİTAK Summer School: Moduli Spaces of Coverings⌗
Date: June 09, 2008 at 09:00
Location: Galatasaray University
GTEM/TÜBİTAK Summer School on Moduli Spaces of Coverings. More info: https://math.gsu.edu.tr/GAMSC/
2007⌗
CIMPA Summer School: Arrangements, Local Systems & Singularities⌗
Date: June 11, 2007 at 09:00
Location: Galatasaray University
CIMPA Summer School on Arrangements, Local Systems and Singularities. More info: https://math.gsu.edu.tr/als/
2006⌗
EMS Summer School: Arithmetic & Geometry Around Quantization⌗
Date: June 05, 2006 at 09:00
Location: Galatasaray University
EMS Summer School on Arithmetic and Geometry Around Quantization. More info: https://math.gsu.edu.tr/agaq/
2005⌗
CIMPA Summer School: Arithmetic & Geometry Around Hypergeometric Functions⌗
Date: June 13, 2005 at 09:00
Location: Galatasaray University
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions. More info: https://math.gsu.edu.tr/agahf/
Past Events by Type⌗
Departmental Seminar⌗
2026⌗
Departmental Seminar - Keremcan Doğan, Gebze Technical University⌗
Date: May 06, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Exceptional Drinfel’d Algebroids and Rackoids
Abstract: String and M-theories dictate new symmetry notions that are absent in point-particle theories. The generalized geometry program extends usual differential geometry in a suitable manner to explain one class of these new symmetries, known as T-duality. In particular, Poisson-Lie T-duality can be understood as arising from different decompositions of the Drinfel’d double of a Lie bialgebra, which is itself a Lie algebra. Extending this to the algebroid setting leads to Drinfel’d doubles of Lie bialgebroids, which are Courant algebroids. In order to explain another class of new symmetries, called U-duality, one needs to further extend these notions. In one of our recent works, we extended Lie bialgebroids and their Drinfel’d doubles to a set-up in which the vector bundles are not dual in the usual sense, and we introduced bialgebroids and their Drinfel’d doubles via a calculus framework on algebroids. In this talk, we use this framework to introduce and construct a specific type of algebroid, which we call exceptional Drinfel’d algebroids. We prove that these are algebroid versions of exceptional Drinfel’d algebras, which have recently been defined in the physics literature in order to extend the Lie bialgebra/T-duality relation to the U-duality case; hence the name. We provide a mathematically rigorous framework to describe these algebras and their algebroid versions in a frame-independent manner, where we use Nambu-Poisson structures and their certain generalizations. Moreover, we introduce exceptional Drinfel’d rackoids, which are global versions of exceptional Drinfel’d algebroids, analogous to the relation between a Lie group and its Lie algebra. As examples, we focus on the $SL(5)$ and $E_{6(6)}$ cases; for the latter we also use another extension called proto bialgebroids, where $H$- and $R$-fluxes are present. Join with Google Meet: https://meet.google.com/cuo-tuyk-hte Or dial: (US) +1 915-247-5177 PIN: 224480191# Learn more about Meet at: https://support.google.com/a/users/answer/9282720
Departmental Seminar - Begüm Ateşli, İTÜ⌗
Date: April 08, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: On the Structural Foundations of Lie Algebroids and Their Higher Analogues
Abstract: This talk is concerned with the structural theory of Lie algebroids and 3-Lie algebroids. After reviewing the basics of Lie algebroids and their connection with Poisson geometry, we introduce a coupling construction based on mutual actions and cocycle terms that produces a Lie algebroid structure on the direct sum of two vector bundles. This bicocycle double cross product construction yields a unified framework for several geometric extensions. We then discuss the analogous construction for 3-Lie algebroids. In the final part of the talk, we explain how a 3-Lie algebroid can be constructed from a given Lie algebroid by using differential operators, Lie and 3-Lie connections, and curvature operators. We also indicate how Poisson Lie algebroids fit into this picture, leading to a Poisson 3-Lie algebroid structure.
Departmental Seminar - Salah Mehdi - Lorrent University, France⌗
Date: March 25, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: From Numbers to Spectrum: A guided ramble through the Langlands Program and Locally symmetric spaces
Abstract: Robert Langlands, a Canadian mathematician, introduced in the late 1960s a remarkable set of conjectures aimed at unifying various areas of mathematics, including number theory, geometry, and spectral analysis. Since then, the Langlands program has been at the forefront of intense research, inspiring several Fields Medals and other prestigious awards. In this talk, designed to be accessible to a broad audience, I will first outline the key ideas and motivations behind Langlands’ unifying program, and then present some recent results on locally symmetric spaces, highlighting how they fit into the broader landscape of Langlands conjectures and representation theory. Some of these results come from joint work with Martin Olbrich.
Departmental Seminar: Cem Yetişmişoğlu, Istanbul Medipol University⌗
Date: March 18, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Graded manifolds and their applications in physics
Abstract: In this talk we will define (Z/2Z)-graded manifolds, and certain geometrical structures on them. We will then focus on two applications in which these manifolds appear in physics literature. In the first one, we will be talking about how discrete systems, their dynamics, and their measurements can be described by a generalization of symplectic graded manifolds (math-ph:2311.05711). In the second application, we will be talking about how such manifolds appear in formulations of algebroids and their Drinfel’d doubles which encode symmetries of stringy geometries (hep-th:2409.11973)
Matematik Bölümü Genel Semineri - Tekin Dereli - Özyeğin Üniversitesi, Koç Üni. (Emeritus)⌗
Date: March 04, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye - Aydın Doğan Conference Room
Başlık: 21. Yüzyılda Einstein’ın izinden gidebilecek miyiz?
Özet: Einstein’in genel görelilik teorisi 1916 yılına dayanmaktadır ve kütleçekimi anlayışımız için dinamik bir uzay-zaman yapısı çerçevesinde matematiksel bir temel sağlar. Teorinin en çarpıcı öngörüleri arasında kütleçekimsel dalgaların varlığı, genişleyen Evren modelleri, kara deliklerin gerçekliği yer almaktadır. Nitekim bu konuların önemi, son on yılda üç Nobel Ödülü kazanarak kanıtlanmıştır. Bu durum, söz konusu başlıkların gelecek nesil fizikçilerin temel çalışma alanları olacağına dair kuvvetli bir göstergedir. Öncü bir ülke olarak bu çalışmalara neden ve nasıl katılmamız gerektiğine dair birkaç söz söyleyeceğiz.
Departmental Seminar: Öznur Turhan⌗
Date: February 11, 2026 at 13:00
Location: Galatasaray University, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Bekka's (c)-regularity condition and families of line singularities with constant Lê numbers
Abstract: We show that the natural stratifications arising from certain deformation families of line singularities with constant Lê numbers satisfy Bekka’s (c)-regularity condition. As a corollary, we obtain that these families are topologically equi-singular. Similar results for families of isolated singularities were established by Abderrahmane. This is a joint work with Christophe Eyral.
2025⌗
Departmental Seminer: Sibel Şahin (Mimar Sinan University)⌗
Date: December 17, 2025 at 12:00
Title: Approximation Numbers of Differences of Composition Operators
Abstract: In this talk we will consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H2(D). The component structure of bounded
composition operators is a widely studied area and in order to understand whether two composition operators belong to the same component, it is important to understand how their difference behaves (compact, bounded etc.). One of the key elements in understanding the
behavior of an operator is to consider its approximation numbers since it gives us the information about how much our operator differs from a bounded/compact one. During the talk we will mention how we can combine these two topics in operator theory and how one can obtain optimal upper and lower bounds for approximation numbers of differences using classical invariants like Bernstein and Gelfand numbers and specific choices of Blaschke products from the underlying function space.
References
[1] G. Lechner, D. Li, H. Queff ́elec, L. Rodriguez-Piazza : Approximation numbers of weighted composition operators. Journal of Functional Analysis 274, 1928–1958 (2018).
[2] J. Moorhouse, C. Toews : Differences of composition operators. Contemporary Mathematics 321, 207–213 (2003).
[3] H. Queffelec, K. Seip : Decay rates for approximation numbers of composition operators.
Journal d’Analyse Mathématique 125, 371–399 (2015).
Remark: First researcher (a) is supported by The Scientific and Technological Research
Council of T ̈urkiye (TUBITAK)-2219 International Postdoctoral Research Fellowship Program (Project no: 1059B192301690).
Departmental Seminer: Yorgo Şenikoğlu (Galatasaray Üniversitesi)⌗
Date: December 03, 2025 at 12:00
Location: Room H307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Scattering of massive neutrino test elds from a gravitational pulse
Abstract: Linearized Einstein-Weyl equations are solved precisely in the context of
sandwich gravitational waves. The neutrino’s energy-momentum depends
on the geometry and composition of the gravitational pulse when it is scattered.
Since the background remains unchanged at the test field level, the
neutrino’s energy density will exhibit fluctuations between positive and
negative extremes when traversing the sandwich wave. These variations
could provide insights into the behavior of models concerning neutrino
oscillations.
Yıldırım Akbal⌗
Date: June 18, 2025 at 13:00
Location: Galatasaray Üniversitesi, Ortaköy, Ciragan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Towards a Foundational TS Model
Abstract: In this talk we will look at a series of foundational time series (TS) models. Starting with a discussion of classical approaches like ARIMA and their limitations, we will explore why traditional machine learning models often fail in this domain. Introducing “One-for-All”, a model designed to address many of these challenges, we highlight its unique features and training procedure, while addressing its limitations. Finally, we propose some ideas and share some insights to enhance the model’s capabilities over long horizons, ensuring robustness and accuracy in extended time series forecasting.
Pascale Roure (Yıldız Teknik Üniversitesi)⌗
Date: May 14, 2025 at 12:00
Location: Room H306, Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: “A World of Probability”. Hans Reichenbach’s epistemological contribution to logical empiricism in the 1930s.
Abstract: After his dissertation on “The concept of probability in the mathematical representation of reality” (Erlangen 1915), Hans Reichenbach elaborated a probabilistic theory of knowledge aimed at solving the problem of induction, first in the context of the Berlin Group of logical empiricism and after 1933 during his 5-years stay at Istanbul University. His innovative approach among the European empiricists at that time was based on a logic of probability, understood as a logic with a continuous scale of truth-values, in terms of which the two valued logic appears as special case. Reichenbach’s probabilistic theory of knowledge gave rise to vivid discussions in the mid 1930s, that led him to criticize harshly the “positivism” he associated with some representatives of the Vienna Circle, as formulated in his work Experience and Prediction (1938). Drawing on Reichenbach’s writings on the concept of probability and its epistemological significance, my presentation aims to clarify the idiosyncrasy of his reflections and their role in the early development of an analytical philosophy of science or, in Reichenbach’s words, of a “method of analysis of science” (wissenschaftsanalytische Methode).
A. Begüm Bektas (Sloan Kettering Institute)⌗
Date: April 16, 2025 at 12:00
Location: Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye Room: H307
Title: Learning with Kernels: Interpretability, Efficiency, and Applications to HighDimensional Data
Abstract: Inthis talk, I will give a brief introduction to learning with kernels, afundamental area in machine learning. I will then present an overview of tworelated publications from my work. The first focuses on multiple kernellearning (MKL), which combines multiple kernel matrices and a domain relatedinformation source in an optimization model. I will discuss how this method canperform well on high dimensional and highly correlated data, how it can achieveinterpretability, and how it can yield improved outcomes using only one tenthof the data. If time allows, I will also address a well-known limitation ofkernel methods, namely the high computational cost, and introduce MultipleApproximate Kernel Learning, a novel approach that provides scalability and efficiencyby using approximated matrices in place of full kernel matrices in MKL.
Mustafa Topkara (Mimar Sinan Güzel Sanatlar Üniversitesi)⌗
Date: February 26, 2025 at 12:00
Location: Room h307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Limits in the Mapping Class Groupoid of Surfaces
Abstract: One way to investigate surfaces is through their triangulations or, equivalently, the dual ribbon graphs (the ‘modular graphs’) and an operation that relates them (the ‘flip’). In this talk, we will discuss the effect of flips on the ‘infinite punctures’ of a surface and explore possible ways to take limits of such flips.
Cheikh LO - Anta Diop University of Dakar⌗
Date: February 19, 2025 at 12:00
Location: Galatasaray Üniversitesi Ortaköy; H306
Title: ON CHARACTERISTICS OF ISOMETRIES IN HYPERBOLIC GEOMETRY
Abstract: In the first time of the talk we present characteriza-tions of isometries of hyperbolic plane by using some geometric objects. More precisely we show that the curves of constant geodesic curvature-preserving maps are isometries. In the second time we highlight the difference between geodesics and horocycles by showing that an abstract automorphism of the geodesic graph is induced by an earthquake map while that of a horocycle graph is induced by an isometry. Join with Google Meet: https://meet.google.com/mia-pyfu-iqz Or dial: (US) +1 401-753-9621 PIN: 107158657# Learn more about Meet at: https://support.google.com/a/users/answer/9282720
Burak Kaya (Ortadoğu Teknik Üniversitesi)⌗
Date: February 12, 2025 at 12:00
Location: Room h307 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye
Title: Borel distinguishing number
Abstract: In broadest sense, descriptive graph combinatorics is the study of “definable” graphs on Polish spaces that incorporates the descriptive set theoretic point of view into the graph-theoretic point of view. This is usually done by demanding various graph-theoretic objects such as edge relations, colorings, automorphisms to have topological/measure-theoretic properties such as being Borel, projective, continuous, closed and asking to what extent classical results of graph theory generalize to measurable setting. Over the last two decades, numerous interesting results have been proven which demonstrate that this point of view is more than a mere specialization that lead to fruitful ideas. In the first half of this talk, after recalling some basic descriptive set theoretic notions, we shall give a brief overview of some fundamental results in descriptive graph combinatorics. In the second half of this talk, we will cover some new results regarding Borel distinguishing numbers. The results in the second half are from a joint ongoing work with Onur Bilge.
2024⌗
Athanase Papadopoulos: The earthquake metric on Teichmüller space⌗
Date: December 20, 2024 at 11:00
Location: Galatasaray Üniversitesi, Room H303
I will explain new results on the earthquake metric, an asymmetric Finsler metric on the Teichmüller space of a surface. This is recent work with Yi Huang, Ken’ichi Ohshika and Huiping Pan. I will survey the basic properties of this metric, and explain new properties, including incompleteness, asymptotic distance to the boundary and comparisons with the Thurston metric and the Weil-Petersson metric.
Tınaz Ekim (Boğaziçi Üniversitesi): Theory and Computation of the Defective Ramsey Numbers⌗
Date: December 18, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We investigate a variant of Ramsey numbers called defective Ramsey numbers, introduced by Ekim and Gimbel in 2013, where cliques and independent sets are generalized to k-dense and k-sparse sets, both commonly called k-defective sets. Following some defective parameters in general graphs, we focus on the computation of defective Ramsey numbers in some restricted graph classes: cographs, chordal graphs, bipartite graphs, perfect graphs, split graphs, cacti, and triangle-free graphs. We adopt a two-fold approach to tackle defective Ramsey numbers. We provide direct proofs using structural graph theory. When this technique falls short in obtaining new values of defective Ramsey numbers, we use efficient graph enumeration techniques for structured graphs.
Özgür Martin (Mimar Sinan Güzel Sanatlar Üniversitesi): How to train your large AI model at a lower cost?⌗
Date: December 04, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
Stochastic gradient descent (SGD) method and its variants constitute the core optimization algorithms that are used for training large-scale machine learning models. These algorithms achieve very good convergence rates, especially when they are fine-tuned for the application at hand. Unfortunately, this tuning process can require large computational costs. For example, GPT-4 (the core machinery of ChatGPT), was trained using trillions of words of text and many thousands of powerful computer chips. The electric bill for the training was over $100 million. Recent work has shown that these costs can be reduced by choosing the learning rate adaptively. We propose an alternative approach to this problem by using a new algorithm based on forward step model building built upon SGD.
Didier Lesesvre (Université Lille): Packing spheres: piling up oranges… and very modern mathematics⌗
Date: November 27, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
Sphere packing is an extremely old problem, yet both widely applied in various domains and very challenging and active mathematically. From unexpected applications to industry to minimizing quadratic forms, from piling up oranges to the mysterious Einstein hat that tiles the plane in an a-periodic way, from very naive questions to the most modern maths (culminating with the groundbreaking achievement of Maryna Viazovska in 2018 to determine the optimal sphere packing in dimensions 8 and 24), I will present some of the developments and ideas behind these questions. These feature in particular beautifully rich mathematical objects: modular forms, which are at the heart of the “modular magic” used by Viazovska, allowing to make the proof of the sphere packing surprisingly accessible.
Sinan Yıldırım (Sabancı Üniversitesi): Adaptive Online Bayesian Estimation of Frequency Distributions with Local Differential Privacy⌗
Date: November 20, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
We propose a novel Bayesian approach for the adaptive and online estimation of the frequency distribution of a finite number of categories under the local differential privacy (LDP) framework. The proposed algorithm performs Bayesian parameter estimation via posterior sampling and adapts the randomization mechanism for LDP based on the obtained posterior samples. We propose a randomized mechanism for LDP which uses a subset of categories as an input and whose performance depends on the selected subset and the true frequency distribution. By using the posterior sample as an estimate of the frequency distribution, the algorithm performs a computationally tractable subset selection step to maximize the utility of the privatized response of the next user. We propose several utility functions related to well-known information metrics, such as (but not limited to) Fisher information matrix, total variation distance, and information entropy. We compare each of these utility metrics in terms of their computational complexity. We employ stochastic gradient Langevin dynamics for posterior sampling, a computationally efficient approximate Markov chain Monte Carlo method. We provide a theoretical analysis showing that (i) the posterior distribution targeted by the algorithm converges to the true parameter even for approximate posterior sampling, and (ii) the algorithm selects the optimal subset with high probability if posterior sampling is performed exactly. We also provide numerical results that empirically demonstrate the estimation accuracy of our algorithm where we compare it with nonadaptive and semi-adaptive approaches under experimental settings with various combinations of privacy parameters and population distribution parameters. (joint w. Soner Aydın)
M. Akif Erdal (Yeditepe Üniversitesi): Equivariant Fibration Categories via Enrichments⌗
Date: November 06, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We first discuss fibration category structures induced by enrichments in symmetric monoidal categories that are also fibration categories. Then we discuss extension of these structures to equivariant context and show that for a group G and a symmetric monoidal category V which is also a fibration category, under mild conditions the category of G-objects in a V-enriched category admits a nontrivial fibration category structure. Lastly we discuss some examples of such fibration categories and applications.
Atabey Kaygun (Istanbul Teknik Üniversitesi): Distributive Laws and Cross Simplicial Groups⌗
Date: October 16, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
There is a way of writing an algebraic structure (a group or an algebra or a category) as a product of two substructures. This is known as a distributive law, and also as a factorization system. After giving examples, I am going to introduce crossed simplicial groups. Crossed simplicial groups are defined by a distributive law between the simplicial category $\Delta$ and a suitable collection of groups. My main aim is to explain how one can extend the notion of ‘simplicial homotopy’ to crossed simplicial groups. We’ll end with a very interesting example coming from Leibniz algebras that are non-skew-symmetric analogues of Lie algebras.
Özlem Ejder (Koç Üniversitesi): Groups, Geometry, Arithmetic and Dynamics⌗
Date: October 02, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H304
Let a₀ be an integer, let f be a polynomial, and consider the sequence aₙ = f(aₙ₋₁). It is a natural question to ask whether there are infinitely many primes in this sequence. One quickly decides that there are not enough tools at hand to deal with this question and one asks instead about the primes dividing at least one term of the sequence. It turns out that the symmetries of the pre-images of a₀ under the iterates of f play an essential role in the solution of this density question. Motivated by the prime density questions, we study the Galois theory of the iterates of a polynomial (or a rational function). We see fruitful connections between geometry, dynamics, arithmetic, and group theory in this subject. Some of the results presented in this talk are joint work with Y. Kara, E. Özman.
Zeynel Ulusan (Koç University): Exploring the frontier of mathematical reasoning with large language models⌗
Date: May 08, 2024 at 16:00
Location: Galatasaray Üniversitesi, room I222
In mathematics, there are two distinct approaches to reasoning: informal inferences based on simple reasoning and formal derivations through step-by-step proofs. This centuries-old approach to mathematical reasoning has been revolutionized by the advent of computers and symbolic systems. Initially, symbolic systems were developed to construct proofs step-by-step based on formal derivations. Subsequently, with the advent of deep learning, particularly in the form of large language models, we were able to construct neural network-based structures that, like humans, are capable of both inductive and deductive reasoning. It is important to note that both symbolic systems and deep learning systems, in their respective ways, have their own set of successes and failures. This presentation will examine the distinctions between symbolic systems and deep learning-based systems, with a focus on the capabilities of large language models in problem solving, theorem proving, mathematical reasoning, generating new conjectures, and their performance when used with agents. Additionally, it will explore the potential for integrating language models with formal systems and the benefits of this integration.
Sibel Özkan (Gebze Technical University): On Domination Number of Cayley Graphs⌗
Date: April 17, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
A dominating set of ? is a subset D of V , such that every vertex not in D is adjacent to at least one member of D . The domination number ?(?) is the minimum cardinality of a dominating set for ?. An efficient dominating set of ? is an independent subset D of V , such that every vertex not in D is adjacent to exactly one member of D . Observe that if D is an efficient dominating set of ?, then D is also minimum dominating set of ?. There are results on the domination number and finding efficient dominating sets (if exist) on circulant graphs for certain connection sets. Here I will talk about our results on odd-regular circulant graphs and Cayley graphs on different groups by giving the exact domination number when possible or giving a meaningful bound.
Athanase Papadopoulos (University of Strasbourg): Optimal maps between surfaces⌗
Date: March 22, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I109
I will talk about distance functions between surfaces equipped with metrics, and more especially, I will describe recent works on the Thurston metric and the earthquake metric between hyperbolic surfaces. The work on the earthquake metric is joint work with Yi Huang and Ken’ichi Ohshika. The work on the earthquake metric is joint work with Yi Huang, Ken’ichi Ohshika and Huiping Pan.
Ceren Gürkan (Kadir Has University): How do fluids behave, numerical modelling, new fronts, and applications⌗
Date: February 28, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
Numerical modeling replaces the expensive laboratory experiments if not used parallel to those for developing any technology in science and engineering. Numerical models can be used to understand the behavior of fluids that are essential to our existence and heavily involved in cutting edge technology development. For deeper understanding of the air -hence all aerospace industry-, blood flowing through our veins or spacecrafts traveling to Mars accurate numerical modelling of fluids is vital. This is why technology developers have an unending need for more accurate, faster, and cheaper numerical techniques. The principal component of any numerical model is the partial differential equation that defines the physical phenomena of interest. A fundamental prerequisite for an accurate numerical solution is the generation of a high-quality mesh. Nevertheless, despite continuously growing computer power, mesh generation can still be a challenging task that can easily account for large portions of the computational time. As a possible remedy to the mesh generation challenges, so-called cut discretization methods have gained much attention in recent years. In this talk we will first focus on the basics of fluid modelling and then discover the new fronts and exiting applications where fluids are involved.
Çağrı Diner (Boğaziçi University): Seismic Wave Propagation and Representation of Seismic Sources⌗
Date: February 21, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
In this talk, I will first focus on deriving the wave equation for an elastic medium, followed by a discussion on its Green’s function solution, which incorporates the moment tensor representation of seismic sources. The moment tensor, which is a second-rank tensor, characterizes seismic sources by using the slip direction of an earthquake and the fault’s normal. Moreover, the magnitude of an earthquake is proportionally related to the norm of moment tensor. The structure of the space of moment tensor will be explained, along with the elasticity tensor which is a critical component for the moment tensor’s definition.
Zeynep Hassanzadeh (Istanbul Technical University): Data-driven learning of Lie groups⌗
Date: February 14, 2024 at 15:00
Location: Galatasaray Üniversitesi, room I204
The main purpose of this talk is to propose a newly developed stochastic Monte Carlo (MC) linear solver for some large-scale modeling problems that require special linear solvers due to the specific characteristics of these types of problems. The newly developed MC method offers an alternative to costly deterministic linear solvers, presenting advantages in computational time and complexity, including superior features such as parallelization capability. In this presentation, we propose employing the stochastic MC method for initial value problems with time-dependent coefficients, resulting in a hybrid numerical-stochastic approach that demonstrates superior efficiency compared to corresponding numerical methods. However, this method exhibits broad applicability to diverse classes of dynamic mathematical modeling problems, particularly at large scales. Additionally, we aim to explore integrating this method into the well-known Adaptive Neural-Fuzzy Inference System (ANFIS), thereby reducing computational complexity in computing the pseudo-inverse matrix within the iterative least square estimator (LSE) sub-method of the main ANFIS algorithm. It is known that the ANFIS method offers a powerful tool for data science analysis across various domains and applications such as predictive modeling, control systems, data fusion decision-making, and so on. Indeed, this method is a versatile tool, but its specific application depends on the data and problem at hand. In this research, we applied three classes of the newly modified ANFIS method, incorporating enhancements to their respective generating function structures. These models were utilized to forecast the daily prices of target fuel products using datasets sourced from the Thomson Reuters Eikon Refinitiv database.
2023⌗
Çağatay Yıldız (University of Tübingen): Data-driven learning of Lie groups⌗
Date: December 27, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Learning meaningful representations via deep neural networks has been an important challenge for computer vision tasks. Auto-encoders have been among the most popular approaches as they are shown to enable so-called disentangled representations. Unfortunately, most auto-encoder-based methods are built upon no or very little inductive biases and lack a theoretical foundation. This (ongoing) work aims to provide insights into how group theory could be beneficial for learning modular representations. Given object-centric datasets, we show how to learn latent matrix Lie groups that model underlying transformations the objects undergo within an auto-encoder framework. The resulting framework learns (almost perfectly) disentangled group actions on toy datasets.
Sylvain Lavau (Aristotle University of Thessaloniki): Singular foliations and Lie ?-algebroids⌗
Date: December 20, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
A singular (or Hermann) foliation on a smooth manifold M can be seen as a locally finitely generated subsheaf of the sheaf of vector fields on M closed under Lie bracket. We show that if this singular foliation admits a resolution consisting of sections of a graded vector bundle of finite type, then one can lift the Lie bracket of vector fields to a Lie ?-algebroid structure on this resolution. The choices entering the construction of this Lie ?-algebroid, including the chosen underlying resolution, are unique up to homotopy and, moreover, every other Lie ?-algebroid inducing the same foliation or any of its sub-foliations factorizes through it in an up-to-homotopy unique manner. We thus call it the universal Lie ?-algebroid of the singular foliation. For a real analytic or holomorphic singular foliation, it can be chosen, locally, to be a Lie n-algebroid for some finite n. We will show that this universal structure encodes several aspects of the geometry of the leaves of a singular foliation, and that it allows to extend to the singular context some notions (e.g. characteristic classes) until now only defined for regular foliations.
Mounir Nisse (Xiamen University Malaysia): Singularities and Rearrangement of Knots Via (Co)amoebas⌗
Date: December 13, 2023 at 15:00
Location: Online
Amoebas (resp. Coamoebas) are the image of analytic subsets of the complex algebraic torus under the logarithmic map (resp. argument map) coordinate-wise. In this talk, we open a way relating deformations of class of germs of complex algebraic plane curves diffeomorphisms to rearrangement of links. Indeed, we realize any torus link as the union of the one-dimensional connected components of the set of critical values ??of the argument map restricted to a complex algebraic plane curve. This gives the first relationship between knot theory and coamoebas theory. Moreover, it gives an explicit description of the topology and geometry of links corresponding to singularities.
Salah Mehdi (University of Lorraine): From Fourier series to asymptotics of characters : a glimpse into Lie theory⌗
Date: December 06, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
In 1822, the French mathematician and physicist Joseph Fourier published his seminal treatise Théorie analytique de la chaleur in which he introduced expansions of periodic functions and solved the heat equation on R. Since then, Fourier series and Fourier transforms have been used successfully and extensively in many areas of fundamental and applied sciences. Harmonic analysis aims to generalize Fourier analysis on topological spaces on which a group acts. Group actions lay at the confluences of Mathematics and Physics, their study is the purpose of representation theory of Lie groups. I will explain the ins and outs of Lie theory, and sketch a few of its many tremendous applications. In particular, I will describe how representation theory relates objects of different nature such as orbits, characters and Dirac operators. These recent results are based on joint work with Pavle Pandzi´c, David Vogan and Roger Zierau.
Türkü Özlüm Çelik (Koç University): Algebraic Curves, Computer Algebra and Integrable Systems⌗
Date: November 22, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Algebraic curves have significant applications in the study of the Kadomtsev-Petviashvili hierarchy, which is a universal integrable system that describes shallow water waves. The corresponding finite-genus solutions are expressed in terms of the Riemann theta function. The theta function degenerates as the curve becomes more singular, leading to soliton and rational solutions. These solutions, in turn, characterize the curves in the moduli space of abelian varieties, thus providing a solution to the Schottky problem. To better understand the bilateral connection, we explore various perspectives in computational algebraic geometry, including transcendental and combinatorial approaches, while also utilizing mathematical software. Our study yields new results and insights, along with future directions for research in this field.
Mark Spivakovsky (Toulouse Paul Sabatier University): On the Casas–Alvero conjecture⌗
Date: November 15, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Let k be a field, d a strictly positive integer and x an independent variable. Let f?k[x] be a monic polynomial of degree d. For i?{1,…,d-1}, let f(i) denote the i-th derivative of f (the i-th Hasse derivative in case char k>0). Assume that for all i?{1,…,d-1} the polynomial f(i) has a non-trivial common factor with f. The Casas–Alvero conjecture asserts that, assuming char k=0, there exists a?k such that f(x)=(x-a)d. If char(k)=p>0, the conjecture is false in general. Let us write CAd,p for the statement “The Casas-Alvero conjecture holds for polynomials of degree d over fields of characteristic p”. The following equivalences are known for each d: CAd,0 holds ?CAd,pholds for some prime number p?CAd,p holds for all but finitely many primes p. A prime number p is said to be a bad prime for d if CAd,p is false. In this talk we will discuss an approach to the conjecture that consists in first proving it for some small degree d, compiling lists of bad and good primes for that d and then deducing the conjecture for all the degrees of the form dpl, where l is a positive integer and d a good prime for d. At the end of the talk we will mention a recent result (joint with D. Schaub) that gives a long (but not exhaustive) list of good primes for each d.
Adam Ouzeri (Galatasaray University): A theoretical and computational framework for upscaling epithelial subcellular dynamics to tissue mechanics⌗
Date: November 08, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
Recent observations across various species have revealed a rich phenomenology of epithelial mechanics arising from the active-viscoelasticity and turnover of the actomyosin cortex. However, a link between the subcellular cortical dynamics and the tissue scale response has been lacking in theoretical models of epithelia. For instance, in classical vertex models, a phenomenologically motivated work function governing the vertex dynamics (Alt et al, Philos. Trans. R. Soc. Lond., B, Biol. Sci., 2017) often lacks a direct connection to the microscopic subcellular physics. In this talk, I will present a new formalism, coined active-gel tissue model (AGTM), which bridges the active-gel models of the actomyosin cortex taking into account the active contractility of the cortex, the viscoelastic relaxation due network remodelling and the turnover of its constituents, with vertex-like models at a tissue scale. By solving the active gel on each of the curved faces of a 3D tissue, we show that this unified framework systematically links subcellular cortical dynamics with tissue mechanics, and ties to a common subcellular origin a number of seemingly disconnected dynamical tissue behaviours such as stress relaxation following step-strain manoeuvres (Casares et al., Nat. Mat. 2015, Khalilgharibi et al, Nat. Phys., 2019), buckling and transient buckling upon compression (Wyatt et al, Nat. Mat., 2020), pulsatile contractions during Drosophila dorsal closure (Solon et al, Cell, 2009), spontaneous curling (Fouchard et al, PNAS, 2020) and active superelasticity (Latorre et al, Nature, 2018). This framework is compatible with more elaborate dynamical models of the cytoskeleton, of adhesion complexes and their interaction, and thus serves as a general background for combining more complex multi-species models accounting for regulatory networks and junctional rearrangements, potentially providing a mechanistic understanding of active non-linear response of tissues with cell level resolution.
José Luis Cisneros-Molina (National Autonomous University of Mexico): Indices of vector fields for mixed singularities⌗
Date: October 18, 2023 at 15:00
Location: Galatasaray Üniversitesi, room H304
A mixed function is a real analytic function f:Cn›C in the complex variables z1,…,zn and their conjugates ¯z1,…,¯zn. In this talk we define an integer valued index for vector fields v with isolated singularity at 0 on real analytic varieties Vf:=f-1(0) defined by mixed functions f with isolated critical point at 0. We call this index the mixed GSV-index and it generalizes the classical GSV-index defined by Gomez-Mont, Seade and Verjovsky, i.e., if the function f is holomorphic, then the mixed GSV-index coincides with the GSV-index. Furthermore, the mixed GSV-index is a lifting to Z of the Z2-valued real GSV-index defined by Aguilar, Seade and Verjovsky. As applications we prove that the mixed GSV-index is equal to the Poincar'e-Hopf index of v on a Milnor fiber. If f also satisfies the strong Milnor condition, i.~e., for every ?>0 (small enough) the map f?f?:S?\Lf›S1 is a fiber bundle, we prove that the mixed GSV-index is equal to the curvatura integra of f defined by Cisneros-Molina, Grulha and Seade based on the curvatura integra defined by Kervaire.
2022⌗
Elif Üsküplü (University of Southern California): TBA⌗
Date: December 14, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Şafak Özden (Tulane University): TBA⌗
Date: December 07, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Mesut Ürün: TBA⌗
Date: November 30, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Jose Seade (National University of Mexico (UNAM)): TBA⌗
Date: November 23, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Figen Öztoprak Topkaya (Istanbul Technical University): TBA⌗
Date: November 16, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
TBA: TBA⌗
Date: November 09, 2022 at 16:00
Location: Galatasaray Üniversitesi, room H304
TBA
Daniel Massart (Université de Montpellier): TBA⌗
Date: November 09, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
TBA
Soner Aydınlık (Doğuş University): Nonlocal Vibration Analysis of 3-D Plates Using Riesz-Caputo Fractional Derivative⌗
Date: November 02, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
In this study, nonlocal vibration analyzes of 3-D plates modeled are performed with the help of fractional mechanics. The Riesz-Caputo fractional derivative is used to define nonlocality without using kernel functions. The frequency spectrum and mode shapes of the plates are investigated for different fractional derivative orders ($\alpha$) and different length scale parameters (l). The main contributions of these studies are that the nonlocal approach considering fractional analysis give results closer to the experimental results than the classical theory.
Ferhat Kürüz (Istanbul Gelişim University): On a special family cyclic codes and their applications⌗
Date: October 26, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
Coding theory is a field that allows us to construct methods to transfer and store data in a way that can detect and correct corruptions that may occur during the transmission process. Algebraic coding theory uses algebraic structures to construct these methods. Cyclic codes, which are very useful due to their algebraic properties, have a central importance in algebraic coding theory. m-adic residue codes are a type of codes that generates cyclic codes with the help of residue classes. After briefly talking about algebraic coding theory, I will describe cyclic codes and m-adic residue codes. Then, after briefly summarizing the DNA codes, I will explain the relationship between m-adic residue codes and these codes. Finally, I will talk about quantum codes and explain their relationship with m-adic residue codes.
Tülay Ayyıldız Aksoy (Karadeniz Technical University and Istanbul Technical University): Polynomial Real Root Certification using Hermite Matrices over Q⌗
Date: October 12, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H304
Polynomial systems can be solved reliably using numerical homotopy methods. These methods return numerical approximations to solutions, and all the implementations validate the solutions heuristically. Therefore, the output, the approximate solutions of polynomial systems are not certified. Even though the approximate solutions work well in practice, they cannot be used in critical applications, especially in pure mathematics or when high precision is needed (e.g. Surgical Robot arm applications). Let I be a zero dimensional and radical ideal generated by m polynomials with exact rational coefficients. Assume that we are given approximations for the common exact roots. In this talk, we show how to construct and certify the rational entries of Hermite matrices for I from the approximate roots. Furthermore, we represent a method to certify the real roots of the given polynomial system using the signature of Hermite matrices.
Asgar Jamneshan (Koç University): The structure of arbitrary Conze-Lesigne systems⌗
Date: May 25, 2022 at 15:00
Location: TBA
Conze-Lesigne systems are abelian measure-preserving dynamical systems which are isomorphic to their second Host-Kra-Ziegler factors. These factors (and their versions of higher order) are relevant ?in multiple recurrence and related topics in additive combinatorics (e.g. Szemeredi’s theorem). In this talk, we present a structure theorem for Conze-Lesigne systems for actions of an arbitrary countable discrete abelian group, describing such systems as an inverse limit of translational systems G/L, where G is a locally compact nilpotent group of nilpotency class 2 and L is a lattice in G. Such structure theorems were previously known in the important special cases of finitely generated abelian groups by work of Conze and Lesigne and direct sums of finite fields by work of Bergelson, Tao, and Ziegler. We will review some of this literature by way of illustrating examples. If time permits, we present an application of our structure theorem to give a qualitative proof of the inverse theorem for the Gowers U^3-uniformity norm of an arbitrary finite abelian group via a correspondence principle. This talk is based on work jointly with Shalom and Tao. I will introduce and motivate the topic to a general mathematical audience in the first half of my talk.
Yasemin Kara (Boğaziçi University): Solving Fermat Type Equations Via Modular Approach⌗
Date: May 11, 2022 at 15:00
Location: TBA
The asymptotic Fermat conjecture(AFC) states that for a number field K and for sufficiently large primes, the equation x^p+y^p+z^p=0 has only trivial solutions. The strategy which is referred as the “modular method” to solve the Fermat equation, used by Wiles in his famous proof, can be adapted to attack AFC and its several different generalizations. Similar results are quite rare for other Fermat type equations such as x^p+y^q=z^r although the solutions of this equation have been studied over rationals. In this talk, I will mention some recent asymptotic results for the classical Fermat equation as well as some other Fermat type equations over number fields. This talk is based on joint works with Isik and Ozman.
Kevin Buzzard (Imperial College London): Teaching proofs to a computer⌗
Date: April 20, 2022 at 15:00
Location: Microsoft Teams
We all know about computer algebra packages like Maple or Matlab, which can be used to do calculations. But there are other computer programs called things like Coq or Lean or Isabelle/HOL, which can be used to check or generate mathematical proofs. Such systems have existed for decades but it is only recently that the research mathematical community have begun to take them seriously. I will give an overview of what has been happening over the last few years, and also why I think it might begin to matter to our community. I don’t think that computers will be automatically proving the Riemann Hypothesis any time soon, but I do think that maybe they will soon be able to help us with our research, in areas where Maple and Matlab are no use. I will assume the audience has a basic mathematical background but I will not assume any knowledge of computers or computer proof systems.
Hatice Boylan (Istanbul University): The sum of all natural numbers, prime numbers and other mysteries⌗
Date: April 06, 2022 at 15:00
Location: Microsoft Teams
What is the value of the infinite sum 1+2+3+4+…, how can we make sense of it and why should we care? In these considerations we end up at some point at the Riemann zeta function which encodes the mysteries of the distribution of primes. We explain how Riemann deciphered part of this encoding and mention some relations to modern physics.
Ezgi Kantarcı Oğuz (Boğaziçi University): Rank Polynomials of Fence Posets are Unimodal⌗
Date: March 23, 2022 at 15:00
Location: Galatasaray University, room H306
We prove a conjecture of Morier-Genoud and Ovsienko that says that rank polynomials of the distributive lattices of lower ideals of fence posets are unimodal. We do this by introducing a related class of circular fence posets and proving a stronger version of the conjecture due to McConville, Sagan and Smyth. We show that the rank polynomials of circular fence posets are symmetric and conjecture that unimodality holds except in some particular cases. We also apply the recent work of Elizalde, Plante, Roby and Sagan on rowmotion on fences and show many of their homomesy results hold for the circular case as well (joint work with Mohan Ravichandran).
Zehra Bilgin (Fatih Sultan Mehmet Vakıf University): TBA⌗
Date: March 09, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H306
(Abstract not available in text)
Fatma Çiçek: TBA⌗
Date: February 23, 2022 at 15:00
Location: Galatasaray Üniversitesi, room H306
(Abstract not available in text)
Ahmad Rafiqi (Galatasaray University): Characterizing Abelian differentials and pseudo-Anosov maps as permutations of integers⌗
Date: January 26, 2022 at 15:00
Location: Galatasaray University, room A324
Thurston’s theory of homeomorphisms from a compact surface of genus greater than one to itself, classifies such maps (and their mapping classes) into three types: periodic, pseudo-Anosov, or reducible - where the surface decomposes into pieces on which the restrictions of the map are either periodic or pseudo-Anosov. The pseudo-Anosov case is thus of great interest in studying these maps. In this case, an integrable quadratic holomorphic differential exists on the surface w.r.t. a Riemann surface structure. When the foliations of the quadratic differential are orientable, namely when there is an Abelian differential preserved by the map, we will characterize the structure of the surface and the pseudo-Anosov map in terms of a permutation of integers.
Türkü Özlüm Çelik (Boğaziçi University): Algebraic Curves to their Jacobians and back⌗
Date: January 12, 2022 at 15:00
Location: Microsoft Teams
We approach the Torelli problem of reconstructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design machinery to solve this problem effectively, which builds on methods in numerical algebraic geometry. We verify these methods via numerical experiments with curves up to genus 7. This is joint work with Daniele Agostini and Demir Eken.
2021⌗
Özlem Ejder (Boğaziçi University): Isolated points on Modular Curves⌗
Date: December 29, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
One of the oldest areas of mathematics is the study of integer or rational solutions to polynomial equations with integer coefficients and it remains active till today. The most natural question we can ask about such an equation is whether its set of rational solutions is finite or infinite. This can be determined by the genus of the curve defined by such equations. In particular, if the genus is greater than one, there are finitely many rational points on a curve. What happens when one allows for solutions involving square-roots of integers or cubic roots? Perhaps in general all complex numbers that are roots of a degree d polynomial? We call such solutions of degree 2,3 or d in general. In this talk, we will discuss when a curve has infinitely many degree d points focusing particularly on points on modular curves
Gönenç Onay: TBA⌗
Date: December 22, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
(Abstract not available in text)
Can Ozan Oğuz (Gebze Technical University): Induction and restriction on symmetry groups of binary trees⌗
Date: December 08, 2021 at 15:00
Location: Galatasaray Üniversitesi, room A324
Symmetry groups of binary trees are isomorphic to iterated wreath products of symmetric groups of order two. In our collaboration with Mee Seong Im, our aim was to describe the relations between induction and restriction on representations of this tower of groups, which embed into each other. Even though we didn’t get a full description of the relevant category, we have partial results concerning the vector space and algebra structure of certain hom spaces. In the talk I will focus on the origin of the problem and various approaches we found helpful during our research.
2019⌗
Nigar Tuncer (Bilgi University, İstanbul): The Principles of Topofold: designed modular biomolecular folds⌗
Date: May 08, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Biopolymers are able to form many complex nanostructures. Nature uses folded proteins as carriers of functional properties or interactions with other biopolymers. Bacause of complex interplay of interactions it is very hard to predict the tertiary structure from the primary structure. Designing completely new protein fold is even more challenging. In this talk, we overview a self-assembly strategy for single-chain polypeptide tetrahedron assembled from coiled-coil segments.
José Cidade Mourao (Instituto Superior Tecnico, Lisbon): Complex Symplectomorphisms, Kahler Geodesics and Representation Theory.⌗
Date: April 19, 2019 at 10:00
Location: Galatasaray Üniversitesi FEF 8
The geodesics for the Mabuchi metric on the space H of Kahler metrics on a compact symplectic manifold M correspond to solutions of a homogeneous complex Monge-Ampere (HCMA) equation. The space H is an infinite dimensional analogue of the symmetric spaces of noncompact type G_C/G for compact Lie groups G. In H the role of G is being played by the group of Hamiltonian symplectomorphisms. I will describe a method for reducing the relevant Cauchy problem for the HCMA eq with analytic initial data to finding a related Hamiltonian flow followed by a “complexification”. For Hamiltonian G-spaces, with G-invariant Kahler structure, the geodesic corresponding to the norm square of the moment map or its Hamiltonian flow in imaginary time (= gradient flow for the changing metric following the geodesic) leads to the convergence of the holomorphic sections to sections supported on Bohr-Sommerfeld leaves. For M=T*G, starting from the vertical or Schrodinger polarization, one obtains the Segal-Bargman-Hall coherent state transform.
Lorenzo Ramero (Université de Lille): Les presques anneaux⌗
Date: April 10, 2019 at 15:30
Location: Galatasaray Üniversitesi FEF 8
Les presques anneaux trouvent leur origine dans les travaux de Faltings sur la théorie p-adique de Hodge, où ils fournissent un outil clé pour le preuve de son théorème de presque pureté, qui à son tour est une profonde généralisation d’une observation remontant à l’rticle fondateur de Tate sur les groupes p-divisibles. Plus recemment, les presques anneaux sont devenus le socle sur lequel Scholze a bati sa théorie des anneaux et espaces perfectoides, l’une des plus spectaculaires trouvailles de la géométrie arithmétique des dernières années. Dans mon exposé j’introduirai les presques anneaux et j’essayerai d’expliquer comment ils sont utilisés dans la théorie p-adique de Hodge et dans la théorie des espaces perfectoides.
Pierrette Cassou-Noguès (Université de Bordeaux): Structure de l’arbre à l’infini d’un polynôme à deux variables⌗
Date: April 10, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Il s’agit de classifier les polynômes à l’aide de la structure de leur arbre à l’infini. Après avoir rappelé la notion d’arbre àl’infini d’un polynôme àdeux variables, nous introduisons des structures simples dans cet arbre, que nous appelons des peignes. Le résultat principal que nous énonçons est le fait que le nombre de peignes est inférieur ou égal à 1+2g, où g est le genre de la courbe générique. Dans le cas des polynômes rationnels, à l’origine de cette étude, on obtient un arbre qui consiste en un seul peigne. A la fin de l’exposé, nous étudions le cas où il existe des dicritiques de degré 1 et nous retrouvons les arbres des polynômes rationnels simples. (travail commun avec Daniel Daigle, Université de Ottawa)
Hakan Ayral (Galatasaray Üniversitesi): Convolutional, Recurrent and Deep Neural Networks⌗
Date: March 20, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
Deep Neural Networks are artificial neural networks with a specific topology belonging to a family of such topologies. Use of many layers with gradually decreasing number of neurons, and use of some specialized prediction and training methods are characteristic of DNNs. Prominent differences between regular ANNs and DNNs consist of highly increased use of layers in specific arrangements, use of specific nonlinear (i.e. ReLU), convolutional or lossy maps to link these layers, and use of specific algorithms (i.e. regularization) to prevent otherwise unexpected problems (i.e. vanishing/exploding gradients) during training. For feature extraction and transformation, each layer uses the output from the previous layer as input in order to learn multiple levels of representations that correspond to different levels of abstraction which forms a hierarchy of concepts. Each layer learns to transform its input data into a slightly more abstract and composite representation; deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning architectures are often constructed with a greedy layer-by-layer method. Deep learning models are vaguely inspired by information processing and communication patterns in biological nervous systems, but they have too many structural and functional differences from biological brains, which make them incompatible with neuroscience evidences. (latter is a separate field called biologically plausible Spiking Neural Networks) The “deep” in “deep learning” refers to the number of layers through which the data is transformed. Deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output; hence it describes potential causal connections between input and output. For feedforward NNs, the depth of the CAP is that of the network; for recurrent NNs a signal may propagate through a layer multiple times, thus CAP depth is potentially unlimited. DNNs are interpreted in terms of the universal approximation theorem and probabilistic inference: For DNNs the universal approximation theorem concerns with information holding the capacity of bounded width, unbounded depth networks. It’s been proven that a DNN satisfying some lower bound constraint on layer width can approximate any Lebesgue integrable function. (Lu, Z. et al., 2017 The Expressive Power of Neural Networks) The probabilistic interpretation features inference and optimization concepts; it considers the activation nonlinearity as a cumulative distribution function. This interpretation led to the introduction of dropout as regularizer in NNs.
Camille Plénat (Aix Marseille Université): Toric embedded resolutions of simple singularities via jet schemes⌗
Date: March 06, 2019 at 14:00
Location: Galatasaray Üniversitesi I219
(Joint work with H. Mourtada) Abstract: One of the aim of Nash’ paper on the arcs spaces (1968) was to understand res- olutions of singularities via the arcs living on the singular variety; in particular he wanted to give a one to one correspondence between families of arcs and es- sential exceptionnal divisors. J.Fernandez de Bobadilla and M.Pe Pereira (2011) have shown that such a bijective correspondence for abstract resolutions of singular surfaces. But the proof does not give a constructive way to get the resolution from the arcs space. With H.Mourtada, we construct an embedded toric resolution of simple singularities from their jets schemes. It is the result I will discuss in the talk.
Mohammad Sadek (Sabancı University): How long can a curve capture a sequence?⌗
Date: February 27, 2019 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In this talk we consider a number-theoretic question that interrelates two group structures. An arithmetic progression sequence on rational numbers carries a pattern that can be imitated in the universe of algebraic planar curves. We start with introducing algebraic curves, with due attention to elliptic curves, then we discuss some of the aspects of the arithmetic on these curves. We dene what we mean by an arithmetic progression sequence within the globe of algebraic planar curves. We then display some of the old and recent developments in the theory. Specically, we discuss the possibilities for the length of these progression sequences. Finally, we present some open questions that currently intrigue researchers.
Mee Seong Im (United States Military Academy): Almost-commuting varieties with a flag⌗
Date: February 06, 2019 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In the construction of Hamiltonian reductions in symplectic geometry, interesting and rich connections to Hilbert schemes, Calogero-Moser spaces, and rational spherical Cherednik algebras have emerged over the last two decades. A Borel analogue of the classical general linear group construction (realized after a reduction from the cotangent bundle of enhanced Grothendieck-Springer resolutions) potentially opens doors for its connections to isospectral Hilbert schemes, flag Hilbert schemes, and other algebraic varieties, that are important to geometric representation theory, algebraic combinatorics, and quantum topology. Our construction can also be realized by certain quiver flag varieties, appearing in the geometric interplay in quiver Hecke algebras that categorify quantum groups. I will discuss a Borel analogue of the cotangent bundle of the extended general linear Lie algebra, discussing the complete intersection of the zero fiber of a moment map (as conjectured by Thomas Nevins), an enumeration of the irreducible components, and a Borel analog of an almost-commuting scheme appearing in the study of Calogero-Moser systems. No background is necessary and I will give plenty of examples throughout my talk. This is joint with Travis Scrimshaw.
2018⌗
Nermine El Sissi (The American University in Cairo): A Combinatorial Interpretation of the LDU-Decomposition of Totally Positive Matrices and their Inverses⌗
Date: December 19, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Hironori SHIGA (Chiba university): A K3 modular function induced from a simple K3 singularity⌗
Date: December 19, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Bruno Deschamps (Université du Mans): Regarding a weak inverse Galois problem⌗
Date: December 12, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In the works of E. Fried and J. Kollár in 1978 and of M. Fried in 1980, it has been shown that any finite group is the automorphisms group of a finite extension of the field of the rational numbers. This is a positive answer to a weak form of the traditional Inverse Galois Problem of Galois theory, which ask if, whether or not, every finite group G appears as the Galois group of a Galois extension of Q. Since the work of Fried- Kollár/Fried, several advances have been made on this weak form. The most recent is from 2017 and is due to E. Paran and F. Legrand who show that this weak form is actually true on any Hilbertian field. In a recent work with François Legrand, we explain how to provide examples on non-Hilbertian fields. In particular, we show that for any finite group G there exists a field k on which the weak form of the Inverse Galois Problem is true but such that G is not Galois over k. This result thus shows the gap that exists between the Inverse Galois Problem and its weak form.
Mehmet Akif Erdal (Université Bilkent): Realizability of vector bundles by normal bundles of manifolds⌗
Date: November 28, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Given a Poincaré complex $X$, we say a bundle $\xi$ over $X$ is realized by the normal bundle of a manifold $M$, if $\xi$ is pulled back from the normal bundle of $M$ along a homotopy equivalence $X\rightarrow M$. The problem of determining such bundles over an arbitrary Poincaré complex is a difficult problem and is related to classical problems of surgery theory. In this talk, we will discuss some methods of approaching to this problem and talk about solutions for certain cases of $X$. In particular, we will discuss conditions on bundles over $X$ that guarantee they are realized by normal bundles of manifolds, for $X$ belonging to a certain class of homology spheres.
Can Ozan Oğuz (Galatasaray Universitesi): Categorification and Heisenberg algebras⌗
Date: November 21, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Categorification is a recent philosophy that aims to enrich current set-based theories by introducing a new layer of morphisms, hence obtaining a category based theory. A classical example is homology theories that recover Euler characteristic through their dimensions, but offer more since one can talk about morphisms between homology groups now. After an introduction to categorification, we will see how this idea was applied to a Heisenberg algebra, through its connection to representation theory of the symmetric group .
Ezgi Kantarci (Galatasaray Universitesi): A Queer Crystal Structure on Shifted Tableaux⌗
Date: November 07, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Crystal bases were introduced by Kashiwara in his study of the representation theory of quantized universal enveloping algebras. A crystal graph is a directed, colored graph with vertex set given by the crystal basis and directed edges given by deformations of the Chevalley generators and that encodes information about the corresponding representations and their tensor product. In this joint project with Assaf, we define explicit operators on semistandard shifted tableaux and use Stembridge’s characterizationto show that these operators have a crystal structure, giving a new proof that Schur P-polynomials are Schur positive. We then add queer crystal operators (odd Kashiwara operators) that give the semistandard shifted tableaux of a given shape the structure of a connected queer crystal. We also give axioms for queer regular graphs parallel to Stembridge axioms for type A crystals that give a partial local characterization of queer crystals.
François Apery (Université de Haute Alsace): On an algebraic definition of the Boy surface⌗
Date: October 24, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In 1984, I was able to obtain a parametrization of the Boy surface by eliminating the Whitney umbrellas of the Steiner surface using the so-called hyperbolic confluence of pairs of singularities. As a result, the Boy surface appears to be a real algebraic surface of degree six. However, the construction was a mix of geometry, differential topology and singularity theory. In this talk I want to investigate the question in the complex algebraic geometry field. We intend to characterize the Boy surface as an complex algebraic surface subjected to natural conditions.
Muhammed Uludağ: Mapping Class Groupoids, Thompson’s groups and Outer Automorphism Groups of Free Groups⌗
Date: October 10, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We concoct a uniform treatment of mapping class groupoids and Thompson’s groups thereby introducing their hybrid groupoids. As a by-product we obtain a description of the outer automorphism group of free groups as the isotropy group of a groupoid, which extends the mapping class groupoid of Mosher and Penner. We illustrate some arithmetic aspects of these groupoids at the end of our talk.
Ozlem Beyarslan: Fields with Virtually Free Group Action⌗
Date: May 02, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
This is joint work with Piotr Kowalski. A G-field is a field, together with an action of a group G by field automorphisms. Our purpose is to give an axiomatization of the theory of “generic”, i.e. existentially closed G-fields. If such axiomatization for the class of existentially closed G-fields exists, we call the resulting theory G-TCF. If G is the trivial group then G-TCF is the theory of algebraically closed fields, ACF. If G is the group of integers, then G-TCF exists and its theory is very well studied ACFA, the theory of algebraically closed fields with a generic automorphism. It is also known that G-TCF exist if G is finite, and G is a finitely generated free group. A natural generalization of finite groups and free groups is the class of virtually free groups. Our main theorem says that, when G is a finitely generated virtually free group, then G-TCF exists. We also give field theoretic propertied of G-fields.
Hussein Mourtada: Arc spaces and partition identities⌗
Date: April 25, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
We will show a link between the arc space (which is an algebro-geomtric object) and the identities of partitions of integer numbers: a partition of a positive integer number is simply a way of writing it as a sum of positive integer numbers. Integer partitions have a long and beautiful history in number theory. The link that we will describe, gives a new point of view on known results and gives new identities.
Michel Coornaert: The Garden of Eden theorem: from Conway’s Game of Life to Arnold’s cat⌗
Date: April 11, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
The Garden of Eden theorem was established by Edward Moore and John Myhill in 1963. It states that a cellular automaton is surjective if and only if it satisfies a weak form of injectivity known as pre-injectivity. In 1999, Mikhail Gromov suggested that the Garden of Eden theorem could be extended to a suitable class of hyperbolic dynamical systems. In this talk, I will discuss the classical Garden of Eden theorem as well as some recent results in the direction indicated by Gromov. This is joint work with Tullio Ceccherini-Silberstein.
Ipek Tuvay: Stable equivalence of Morita type and Scott modules⌗
Date: April 04, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
Let G be a finite group, p a prime number and k an algebraically closed field of characteristic p. Modular representation theory of finite groups aims to understand the blocks of kG which are the indecomposable two-sided ideals of the group algebra kG. To achieve this aim many categorical equivalences between module categories of the block algebras are introduced.Among these, we are concerned with the stable equivalence of Morita type. In this talk after a brief introduction to the subject, the role of Scott modules in this picture will be discussed. Then a recent result with a joint work with S. Koshitani among these lines will be presented.
Valentin Burcea: Formal Holomorphic Embeddings Between BSD-Models⌗
Date: March 21, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
I will be talking about the classification problem for Formal Holomorphic Embeddings between Shilov Boundaries of Bounded and Symmetric Domains.
Mohan Ravichanran: Finite free probability⌗
Date: March 07, 2018 at 14:00
Location: Galatasaray Üniversitesi FEF 7
Free probability, introduced by Voiculescu in the early 1980’s is a general method to study asymptotic statistics of random matrices. It also provides a parallel theory of probability with the notion of independence replaced by so called ‘freeness’. Research over the the last three decades has shown the existence of ‘free’ analogues of results ranging from central limit theorems to the existence of Brownian motion to De Finetti type theorems in free probability. Freeness however does not exist in finite dimensions and as such free probability is inherently qualitative in the results it yields for random matrices.In 2015, Adam Marcus proposed a theory called ‘finite free probability’ that seems capable of providing non-asymptotic results. There are several questions that are wide open in this new setting and I will mention some current work of mine that seems to clarify at least one of them.
2017⌗
Atabey Kaygun: Distributive Laws and Unramified Graph Coverings⌗
Date: December 27, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Distributive laws, also known as “factorization systems,” are useful tools. I will start by few examples, and then explain how an unramified graph covering is equivalent to a pair of groupoids linked together with a distributive law. I will also talk about the beautiful Galois theory behind such coverings. Time permitting, I will comment on the homological ramifications of having such pairs.
İlker Savaş Yüce: Isometries of length 1 in purely loxodromic free Kleinian groups and trace inequalities⌗
Date: December 13, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Hakan Güntürkün: Some Results On Line Arrangements⌗
Date: December 06, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We will review some classical problems and results about line arrangements in the real and complex projective plane. For real arrangements, Sylvester-Gallai and orchard problems, Dirac-Motzkin conjecture and some comments about the solutions will be given. For complex arrangements we will describe nets as well as some special arrangements. We will present Melchior’s and Hirzebruch’s inequalities. Finally, after introducing tropical lines, we intend to present some of our own work on the subject.
Nihat Berker: Chateaubriand, Simone de Beauvoir, MIT, and Augmented Mechanics: Education and Research across 3 Cultures⌗
Date: November 29, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Jean-Louis Verger-Gaugry: Limit Problems in Number Theory, Lehmer’s Conjecture and Dynamical Zeta Functions⌗
Date: November 15, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
To dynamical systems of arithmetical origin are associated dynamical zeta functions. Focus will be given to the Rényi-Parry beta-shift and its use for the problem of minoration of the Mahler measure of algebraic numbers (or of the height). In particular the Conjecture of Lehmer, the Conjecture of Schinzel-Zassenhaus and Dobrowolski’s inequality will be considered.
İlhan İkeda: On the Langlands functoriality principle⌗
Date: November 08, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
Let K denote a global field. In the first part of our talk, we shall introduce an unconditional topological group WA_K, which depends only on the global field K,and which is closely related with the hypothetical automorphic Langlands group L_K of K. In the second part of our talk, we shall introduce a new type of parameters and discuss how these parameters are related with the reciprocity and functoriality principles of Langlands.
Nicolas Dutertre: Lispchitz-Killing curvatures of semi-algebraic sets⌗
Date: June 07, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We recall the definition of the Lipschitz-Killing curvatures of submanifolds of $R^n$ and of semi-algebraic sets. We give several Gauss-Bonnet theorems for semi-algebraic sets.
Can Deha Karıksız: Hypercyclicity of Weighted Backward Shifts on Spaces of Real Analytic Functions⌗
Date: May 17, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Roland Bacher: How to poison all the big rats⌗
Date: May 03, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
We construct a “small” subset of points (locations of poison) wich intersects all convex sets of sufficiently large area (the big rats). We outline the higher dimensional generalization and discuss related open questions. Finally, we present perhaps rapidly a connection with phyllotaxis (the connection is mathematical and not based on the fact that leaves of plants are eaten by rats).
Enver Özdemir: Class number of Real Quadratic Fields⌗
Date: May 03, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
In this talk, I will present a relation between the class numbers of imaginary quadratic fields and real quadratic fields. I will talk about prime factors of class numbers of certain quadratic fields and explain how we exploit this to find factors of composite integers.
Mustafa Topkara: Decomposability of Fiber Bundles⌗
Date: April 26, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
A fiber bundle is said to be “indecomposable” if it cannot be expressed as a fiber product of fiber bundles of smaller fiber dimension, and is “stably indecomposable” if its fiber product with any other fiber bundle cannot be decomposed into (i.e. expressed as a fiber product of) fiber bundles of smaller fiber dimension. The talk will be about the relationship between these two concepts.
Oğul Esen: Matching of dynamical systems: With an introduction to Geometric Mechanics⌗
Date: April 19, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
The talk will be consisting of two main parts. In the first one, a gentle introduction to the geometric mechanics will be presented. Accordingly, some basic notions of the theory namely, Lie groups, Lie algebras, Poisson manifolds, and Hamiltonian systems will be summarized. Several examples will be provided. In the second part, we shall address the problem of determining the matched equations of motion of two interacting systems (whose configuration spaces are Lie groups) governing the coupled system starting with the individual equations of motions in Hamiltonian form. The configuration spaces of the systems being Lie groups is imperative here in order to define the mutual actions. We shall present the theory of matched dynamics and particularly write the matched Lie-Poisson equations. It will be shown that the theory of matched dynamics is a generalization of the well-developed semi-direct product theory.
Denis Ibadula: Techniques for computing the Igusa local zeta function of some plain curves⌗
Date: March 15, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 10
The Igusa local zeta function is a generating function which counts, for a fixed prime number p, the number of solutions of polynomial congruence f(x) ? 0 modulo p, p2, p3, and so on. Naturally, such a quantity bears deep relations to other important mathematical ideas from number theory, algebraic geometry and singularities theory. In this work we explore some computational aspects of the Igusa local zeta function associated to the nondegenerate plane cubics over Qp for p? 2,3.
Esengül Saltürk: Self-Dual Codes Over Local Frobenius Rings⌗
Date: March 08, 2017 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Self-dual codes have a rich mathematical theory and they have canonical connections to finite designs and unimodular lattices. We study self-dual and formally self-dual codes over local Frobenius rings of order 16 and give their binary images under a Gray map.
2016⌗
Murad Özaydın: Noncommutative Algebraic Geometry on a Leavitt Path Algebra of Polynomial Growth⌗
Date: November 30, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Algebraic Geometry classically studies the geometry of sets given as the solutions to polynomial equations via the commutative algebra of “regular” functions on this set. According to the Gelfand-Grothendieck philosophy a commutative ring should be thought of as a ring of functions: Complex valued continuous functions for (locally) compact Hausdorff topological spaces (Gelfand-Naimark duality) where the points of the space correspond to maximal ideals; polynomial functions for affine varieties where we need all prime ideals (with the Zariski topology) to keep functoriality. In Connes’s noncommutative geometry noncommutative rings are also regarded as rings of functions. Now there are several candidates for the “points”: maximal ideals, primitive ideals and simple modules (these are equivalent when the ring is commutative). The general consensus is that there are never enough points (for instance to recover the original ring). Leavitt Path Algebras are constructed from the geometric data of a di(rected )graph G. A theorem of Alahmadi, Alsulami, Jain and Zelmanov says that they have polynomial growth if and only if the cycles of G are mutually disjoint. In this case there seem to be enough points (at least for algebraic quantum spheres) after some tweaking of the spectrum (= space of points). While this is a sequel to the seminar by Ayten Koc, familiarity with that talk is not a prerequisite. Relevant concepts will be (re)defined and graduate students are the target audience.
Ayten Koç: Simple Modules of Leavitt Path Algebras of Polynomial Growth⌗
Date: November 23, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
The first half of this talk will be an introduction to LPAs (Leavitt Path Algebras), in particular their representations. In the second half of the talk I’ll try to indicate the recent classification of the simple modules when the LPA has polynomial growth (joint work with Murad Özaydin). The interesting class of Leavitt path algebras of polynomial growth (i.e. finite Gelfand-Kirillov dimension) include the algebraic Toeplitz/Jacobson algebra and algebraic quantum spheres of every dimension. All the relevant terminology will be dened and explained, the talk is aimed at graduate students.
Zehra Balli: Comparaison Numérique Eléments Finis et Méthode Isogeometrique⌗
Date: November 16, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
L’objectif est de comparer deux méthodes numériques. La méthode d’analyse isogéométrique qui est proposée par Hughes en 2005 permet d’établir une relation étroite et cohérente entre la conception assistée par ordinateur (CAO) et l’ingénierie assistée par ordinateur (IAO).
Konstantinos Tyros: Some Density Ramsey type results⌗
Date: October 26, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
The aim of this talk is to present the density versions of the Hales–Jewett Theorem and the Carlson–Simpson Theorem. The Hales–Jewett Theorem is one of the most representing results in Ramsey theory. Its density version was first proved by H. Furstenberg and Y. Katznelson in 1991 using Ergodic Theory. However, since then, combinatorial proofs have been discovered. The Density Hales–Jewett Theorem has as a consequence Szem ´eredi’s Theorem on arithmetic progressions as well as its multidimensional version. The Density Carlson–Simpson Theorem is an extension of the Density Hales–Jewett Theorem and concerns the space of the left variable words.
Özgür Martin: Disjoint dynamics of linear operators⌗
Date: October 12, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Contrary to popular belief, linear dynamical systems can be chaotic. However, in order to find a chaotic linear map, one needs to work on infinite-dimensional metric spaces. We will make an introduction to Linear Dynamics, which is a new and active branch of Functional Analysis. We will also talk about a recent result of Rebecca Sanders and myself about dense manifolds of disjoint hypercyclic operators.
Gönenç Onay: To be announced⌗
Date: April 20, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Olcay Coşkun: To be announced⌗
Date: April 13, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Emine Şule Yazıcı: To be announced⌗
Date: March 30, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Oğuzhan Kaya: To be announced⌗
Date: March 23, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Münevver Çelik: To be announced⌗
Date: March 16, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Hironori Shiga: Number theory through the hypergeometric function⌗
Date: March 09, 2016 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
2015⌗
Yusuf Danışman: To be announced⌗
Date: December 23, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Stamatis Pouliasis: To be announced⌗
Date: December 16, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Çagrı Karakurt: To be announced⌗
Date: December 02, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Hugues Randriambololona: To be announced⌗
Date: November 18, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Zafeirakis Zafeirakopoulos: Polyhedral Omega: A new linear Diophantine system solver⌗
Date: November 11, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative approach based on the Omega operator and explicit formulas for its evaluation with geometric tools such as Brion decomposition and Barvinok’s short rational function representations. In this way, we connect two branches of research that have so far remained separate, unified by the concept of symbolic cones which we introduce. The resulting LDS solver Polyhedral Omega is significantly faster than previous solvers based on partition analysis and it is competitive with state-of-the-art LDS solvers based on geometric methods. Most importantly, this synthesis of ideas makes Polyhedral Omega by far the simplest algorithm for solving linear Diophantine systems available to date. This is joint work with Felix Breuer.
Manfred Hartl: To be announced⌗
Date: November 04, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
To be announced
Jose Luis Cisneros: On the topology of real analytic maps⌗
Date: November 04, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
In this talk we describe a fibration theorem for real analytic maps $f:\mathbb{R}^n\to\mathbb{R}^p$ with arbitrary singularities. Now suppose that $f$ satisfies Thom’s property with respect to a Whitney stratification and let $g:\mathbb{R}^n\to\mathbb{R}^k$ be another real analytic map with isolated singularity at the origin in the stratified sense. We give a Le-Greuel type formula which relates the Euler-Poincaré characteristic of the fibres of $f$ and $(f,g)$. When $f$ and $(f,g)$ are isolated complete intersections we construct an integer valued invariant called the curvatura integra which gives the Euler characteristic of the fibres.
Katsampekis Anargyros: Minimal generators of toric ideals associated to numerical semigroups spanned by four positive integers⌗
Date: October 21, 2015 at 14:00
Location: Galatasaray Üniversitesi FEF 9
Let a1, . . . , a4 be positive integers with gcd(a1, . . . , a4) = 1, and S =< a1, . . . , a4 > be the numerical semigroup generated by a1, . . . , a4. In this talk we determine a minimal binomial generating set for the toric ideal associated to S. Our approach is based on the detection of those binomials and monomials that have to appear in every system of binomial generators of the toric ideal; these special binomials and monomials are called indispensable in the literature.
İlker İnam: Some Problems and A Possible Conjecture On Half-Integral Weight Modular Forms⌗
Date: May 20, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
By the celebrated work of G. Shimura, our knowledge on modular forms of half-integral weight has started to grow. Like in the case of integral weight, they also have arithmetic significance, so both have attracted attention for many years. Recently, one of the breakthrough and very significant results in pure mathematics is the proof of the Sato-Tate conjecture for non-CM modular eigenforms of integral weight (even for Hilbert eigenforms) by Taylor, Barnet-Lamb, Geraghty and Harris. A special case of the Sato-Tate theorem states that signs of coefficients of integral weight Hecke eigenforms are equidistributed. That such should also be the case for half-integral weight forms was conjectured by Kohnen and Bruinier. In this talk, we will discuss the motivation behind this question and explain how the Shimura lift and the Sato-Tate theorem can be exploited to obtain sign equidistribution for certain subsets of the coefficients of half-integral weight eigenforms. Finally, we are interested in the following question: Is it possible state a conjecture like Sato-Tate in the case of half-integral weight modular forms where the question is much more complicated. We will conclude with reporting recent developments on this problem. This is a joint work with S. Purkait (Kyushu), G. Wiese (Luxembourg), S. Arias-de-Reyna (Luxembourg).
Seher Tutdere: On the Torsion-Limit for Algebraic Function Fields⌗
Date: May 13, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk, we first discuss an asymptotic quantity, namely the torsion-limit, for algebraic function fields over finite fields. Then we give some new bounds for the torsion limit of certain towers of function fields over finite fields. Furthermore, using some bounds on the torsion limits, we will give some recent results regarding the construction of arithmetic secret sharing schemes. This is a joint work with Osmanbey Uzunkol.
Mark Spivakovsky: On the Torsion-Limit for Algebraic Function Fields⌗
Date: May 06, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Ekin Özman: The p ranks of Prym varieties⌗
Date: April 29, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This talk is about the relationship between the p-rank of a curve and p-ranks iof the Prym varieties of its cyclic covers in characteristic p>0. Prym variety is a central object of study in arithmetic geometry like Jacobian variety. The goal of the talk is to understand various existence results about Prym varieties such as when g>2, Prym varieties of all unramified cyclic degree ell covers of a generic curve of genus g and p-rank f are ordinary. This is joint work with Rachel Pries
Arzu Boysal: Rational conformal filed theory for pointed stable curves⌗
Date: April 15, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This is a general talk on rational conformal field theory for pointed stable curves. I will give the construction of a rational conformal field theory, and a realization of it in representation theory of affine Lie algebras. Then I will demonstrate how these objects are related to theta functions.
Aydın Aytuna: Parabolic Stein Manifolds⌗
Date: April 01, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for complex manifolds of arbitrary dimension. In the first part of this expository talk, I will compile these notions of parabolicity, compare them and look at some examples. Then I will relate some of these notions to the linear topological type of the Fréchet space of global analytic functions on the given Stein manifold. This will allow us to look at these notions from functional analysis point of view. Finally, I will consider “polynomials” on S-parabolic manifolds and report on some general results about these objects. Most of what I will report in this talk is from joint work with A. Sadullaev.
Emre Mengi: Nonlinear Eigenvalue Problems with Specified Eigenvalues⌗
Date: March 25, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Nonlinear eigenvalue problems have drawn substantial interest in the last two decades in numerical analysis. An important concept regarding them is the backward error, that is how much one has to perturb them so that a specified scalar becomes an eigenvalue. Here we consider the following more general question: given an analytic matrix-valued function, where is a nearest one possessing a set of prescribed eigenvalues located? We derive a singular value optimization characterization for such nearest matrix-valued functions with respect to the operator norm induced by the l2 norm. Our derivation benefits from the root canonical form for a nonlinear eigenvalue problem (generalization of the Jordan canonical from), generalized Sylvester operators, as well as tools from complex analysis. This is a joint work with Michael Karow and Daniel Kressner.
Susumu Tanabé: Geometry of oscillating integrals and Dubrovin conjecture⌗
Date: March 18, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
We consider the oscillating integral defined by the polynomial phase function f(x) with non-degenerate singular points. So called « Lefschetz thimble» can be constructed for each singular point of f(x). This integral can be regarded as Laplace transform of the fibre integral associated to the non-singular variety f^{-1}(c). It turns out (F .Pham) that the intersection indices of vanishing cycles of the variety f^{-1}(c) coincide with those of Lefschetz thimbles (regarded as one dimension higher cycles in a relative homology). We show that the elements of the Stokes matrix defined for the oscillating integral calculates exactly the intersection indices mentioned above. As an application we shall discuss the question on the Stokes matrix S for the quantum cohomology of weighted projective space pour P. Namely we shall present a positive answer to the hypothesis proposed by Boris Dubrovin who predicted that the Stokes matrix S coïncide coincides with the Gram matrix of the exceptional collection of coherent sheaves on P. This is a collaboration with Kazushi Ueda.
2014⌗
Haydar GÖRAL: Algebraic Numbers with Small Height Elements⌗
Date: December 24, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The logarithmic height function is a function that measures the complexity of an algebraic number. This is a fundamental notion at the basis of diophantine geometry. In this talk, we study the set of algebraic numbers with small height elements in terms of model theory, in particular we study their combinatorial properties. Then we investigate how this properties are related to some number theoretic results.
Hadia Messaoudene: Comparaison des classes d’opérateurs; de Joël Anderson et la classe des opérateurs finis⌗
Date: December 18, 2014 at 16:00
Location: Galatasaray Üniversitesi FEF 09
Soit H un espace de Hilbert complexe de dimension infinie, L((H) l’algèbre des opérateurs linéaires bornés définis sur H. La dérivation intérieure induite par A est l’opérateur AX-XA; pour tout X de L(H) . On sait que l’ opérateur identité n’ appartient pas à l’ image de la dérivation de l opérateur A . Le but de cet exposé est d’ étudié les classes d’opérateurs où la distance entre l’identité est l’ image d’une dérivation est minimale( classe de Joël ANderson) Où maximale ( classe des opérateurs finis).
Türker Bıyıkoğlu: Entropy, Assortativity, and Hierarchical Structures in Networks⌗
Date: December 17, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy, the spectral radius of the graph’s adjacency matrix, the Randi'c index, and the degree assortativity. We will see that a hierarchical structure; namely, satisfies a breadth-first search ordering with decreasing degrees is a necessary structure for the extremal graphs that maximize these properties.
İrfan ŞİAP: Algebraic Codes and Some Recent Studies⌗
Date: December 03, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
We present the structure of linear codes over some special chain rings by giving a very quick introduction to error correcting codes. These codes have proved to be a good source for DNA codes. We review some recent studies on these directions and we present some new results. We also point out some open problems and new directions.
Emre Alkan: Special values of L-functions and Diophantine approximation type results on the real line⌗
Date: November 26, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will give a survey on the special values of L-functions and especially the Riemann zeta function. We will show how to approximate real numbers by certain combinations of these special values. This is analogous to the Diophantine approximation of Liouville type numbers by rationals. Some open problems will be mentioned.
Piotr Kowalski: Recovering a field from a one-dimensional structure⌗
Date: November 12, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
I will discuss the model-theoretic notion of interpretability (of one structure in another). For example, the complex field is interpretable in the real field. I will describe my work on algebraically closed fields which are intepretable in ordered fields (joint with Assaf Hasson) and algebraically closed fields which are intepretable in fields with a valuation (joint with Serge Randriambololona).
Michel Lavrauw: Field reduction in finite geometry⌗
Date: November 05, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Based on the well understood concept of subfields in a finite field, the technique called `field reduction’ has proved to be a very powerful tool in finite geometry. In this talk we explain this technique for projective and polar spaces and give some applications.
Olivier Le Gal: O-minimalité et champs de vecteurs⌗
Date: October 30, 2014 at 16:00
Location: Galatasaray Üniversitesi, FEF 09
Dans une première partie, après une introduction rapide à la géométrie o-minimale, on présentera un bref état de l’art des résultats généraux concernant la o-minimalité des trajectoires non oscillantes de champs de vecteurs analytiques. On s’intéressera dans une seconde partie au cas particulier de la dimension trois, où l’on se concentrera sur un résultat de LeGal, Sanz, Speissegger qui montre la o-minimalité des trajectoires non oscillantes appartenant à des pinceaux enlacés.
Deniz Karlı: Stable processes and bounded L^p operators⌗
Date: October 22, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
There is a strong connection between Analysis and Probability Theory. The classical results of Analysis can be obtained by using tools of Martingale Theory, and Brownian motion as the underlying process. Brownian motion is a very specific L'evy process which embraces many ``nice" properties where these properties allows one to reproduce probabilistic alternatives of classical tools. On the other hand, it is possible to study more general L'evy processes with some cost.\ In this talk, we will discuss the question that to what extent we can generalise this process provided that the connection with Analysis is not lost. We will consider some results on bounded linear operators on $L^p(\mathbb{R}^d)$ when the underlying process is taken to be the symmetric stable process which shares some fundamental properties of Brownian motion. We will argue the tools obtained by means of this more general process, and define a new class of harmonic functions to work with. We will also provide a Harnack’s Inequality for this new class of harmonic functions.
Serap Gürer: Topologie algébrique des espaces difféologiques⌗
Date: October 15, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Je vais parler d’études des outils classiques de la topologie algébrique dans le cadre difféologique. Parmi ces outils on se penche particulièrement sur les théories homologiques et cohomologiques généralisées. Un autre objectif est de montrer que les espaces difféologiques offrent un cadre assez naturel afin d’étudier les espaces singuliers. Parmi ces espaces singuliers, on étudie particulièrement les pseudo-variétés contrôlées à la Thom-Mather.
Handan Yıldırım: On Legendrian dualities for the pseudo-spheres in Lorentz - Minkowski space⌗
Date: October 08, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Ian Morrison: GIT of Hilbert schemes of curves linearized in fixed degree and applications⌗
Date: May 23, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
I will describe briefly constructions of families of projective quotients of Hilbert schemes of curves and their applications both as log-canonical models of the moduli space of stable curves and as moduli spaces in their own right for new classes of curves. Because a degree parameter that could be taken ‘‘sufficiently large’’ in prior constructions must be fixed to go further, classical asymptotic methods for analysing stability are no longer effective. After reviewing this setup, I will outline a new method, joint with David Swinarski, for analysing stability in fixed degree for very special varieties, and conclude by explaining how the method is applied in recent work of Jarod Alper, Maksym Fedorchuk and David Smyth.
Cem Güneri: Algebraic Curves over Finite Fields and Their Rational Points⌗
Date: May 21, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
The aim of the talk is to introduce some of the important facts and problems on curves over finite fields. The number of rational points of such a curve is bounded from above by the Hasse-Weil bound and curves reaching this upper bound are called maximal curves. We will pay particular attention to maximal cuves, especially to Hermitian curve since it is the most interesting maximal curve for various reasons.
Tekin Dereli: Quarks: Who will prove the color confinement conjecture? Mathematicians or Physicists?⌗
Date: May 07, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
One of the seven Millenium Problems announced in 2000 by the Clay Foundation was the “mass gap problem”. This problem is still open and concerns the proof of quark confinement conjecture, crucial for the success of Quantum Chromodynamics (QCD) in sub-nuclear physics. After a quick, broad review of QCD as a quantized field theory, I want to comment on its asymptotic freedom and some consequences of UV-IR duality it implies.
Abdenacer Makhlouf: From Generalized integration to Twisted Rota-Baxter algebras⌗
Date: April 30, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Rota-Baxter operators and Rota-Baxter algebras have appeared in a wide range of areas in pure and applied mathematics (probability, combinatorics, Quantum field theory, algebra ….). It turns out that they are closely related to several algebraic structures. In this talk, I will review the historical developments and some basics. Furthermore, I will describe a twisted version and its relationships with some other algebraic structures.
Patrick Popescu Pampu: The kite of a plane curve singularity⌗
Date: April 18, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk I will present the kite of a plane curve singularity : a bidimensional simplicial complex, which embeds canonically in the space of real semivaluations of the local ring of the ambient surface. It allows to compare all the combinatorial encodings used before in the study of such singularities, and to follow geometrically the computations done with them. This is joint work with Garcia Barroso and Gonzalez Perez.
Ferit Öztürk: Real 3-manifolds can be obtained from real 3-sphere via surgery⌗
Date: April 09, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
A real 3-manifold is a 3-manifold with an orientation preserving involution. 3-sphere has a unique real structure with nonempty fixed point set up to equivariant isotopy. It is well-known that every 3-manifold can be obtained from the 3-sphere via +1 and -1 surgeries along a finite collection of knots. In this talk we will prove that any real 3-manifold can be obtained from the real 3-sphere via surgery along a finite “recursively invariant” collection of knots.
Sevgi Perek: İş Yaşamında Yönetici ve Yaşam Koçluğu⌗
Date: March 26, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Serkan Sütlü: Characteristic classes of foliations via SAYD-twisted cocycles⌗
Date: March 12, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk we present our construction of a characteristic map, using a “SAYD-twisted” cyclic cocycle, by which we transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of a certain noncommutative algebra. We carry out the explicit computation in codimensions 1 and 2. In codimension 1, we show how our result matches with the (only explicit) computation done by Connes-Moscovici, and in codimension 2 we present the transverse fundamental class, the Godbillon-Vey class, and the other four residual classes as cyclic cocycles. This is a joint work with B. Rangipour.
Aybike Özer: Dualities in string theory⌗
Date: March 05, 2014 at 15:00
Location: Galatasaray Üniversitesi FEF 10
This talk is comprised of two parts: In the first part, which will be mostly non-technical, I will give a general overview of various duality symmetries in string theory. Then I will explain (part of) our work, where we establish an S-duality relation between the two massive theories obtained from twisted compactifcations of heterotic and IIA string theories down to four dimensions.
2013⌗
Hatice Boylan: Finite dimensional representations of SL_2 over maximal order in a number field⌗
Date: December 25, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
In various applications of automorphic forms it becomes crucial to know the finite dimensional representations of SL_(2,O), where O is a maximal order in a number field. There are amazingly open questions concerning these representations. But recently there has been some progress. In particular, we determined all linear characters of SL(2,O) and we applied the general theory of Weil representations of locally compact abelian groups invented by Weil to generate interesting family of representations of SL(2,O) which possibly contain all finite dimensional representations of SL(2,O) of finite image."
Ayhan Gunaydin: Uniform Versions of the Mordell-Lang Conjecture for Multiplicative Groups⌗
Date: December 18, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The Mordell-Lang Conjecture (MLC) concerns finitely generated subgroups of abelian varieties, however, there are analogous statements in the “non-compact” case: namely the case of the (cartesian powers of) multiplicative group, G_m. (Sometimes, MLC is formulated for semi-abelian varieties to include this case.) In very heuristic terms, in the multiplicative group case, MLC says “the addition doesn’t give new information about finitely generated multiplicative groups of fields.” (This will be made clear in this talk.) We isolate the conlusion of MLC as an abstract property for subgroups of G_m. It turns out that many groups other than finitely generated ones have this property. Moreover, some of them satisfy a uniform version of it. Vaguely, this corresponds to the function field field case of MLC. In this talk, after making everything above more accurate, we prove that certain finitely generated groups have this “uniform” Mordell-Lang Property.
M. Ali Akinlar: On the numerical solution and control of dynamics of some fractional differential equations⌗
Date: December 11, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
This talk separated into three major parts: First overview of fractional calculus, secondly approximate and analytical solutions of some fractional partial differential equations and third analysis of dynamical features of some particular fractional dynamical systems.
Kazim Büyükboduk: An asymptotic Birch and Swinnerton-Dyer Conjecture⌗
Date: December 04, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The conjecture of Birch and Swinnerton-Dyer (BSD) is one of the Clay Millennium problems that links the arithmetic invariants of an elliptic curve to its analytic invariants. Most of this talk will be devoted to explaining the contents of this conjecture and stating its asymptotic variant. As time permits, I will sketch a proof of the asymptotic BSD for CM elliptic curves, which relies on the Iwasawa theoretic study of the Kato-Beilinson elements and the reciprocity law that relates them to relevant L-functions.
Nilay Duruk Mutlubaş: On periodic solutions of a model equation for surface waves of moderate amplitude in shallow water⌗
Date: November 27, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
In this talk, we study the local well-posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water. We use an approach due to Kato which is based on semigroup theory for quasi-linear equations. We also show that singularities for the model equation can occur only in the form of wave breaking, in particular surging breakers.
Mutsuo Oka: Mixed functions of strongly polar weighted homogeneous face type⌗
Date: November 20, 2013 at 16:00
Location: IMBM
Let $f(\bfz,\bar\bfz)$ be a mixed polynomial with strongly non-degenerate face functions. We consider a canonical toric modification $\pi:,X\to \BC^n$ and a polar modification $\pi_{\BR}:Y\to X$. We will show that the toric modification resolves topologically the singularity of $V$ and the zeta function of the Milnor fibration of $f$ is described by a formula of a Varchenko type.
William Gillam: Logarithmic structures in algebraic and differential geometry⌗
Date: November 13, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Logarithmic structures were introduced into algebraic geometry by Kato, Fontaine, and Illusie as a generalization of the toric embeddings studied earlier by Mumford and others. Roughly speaking, the theory furnishes a category where the nicest object is a smooth variety equipped with a normal crossings divisor. We will survey some applications of this machinery in the construction and study of various moduli spaces and in the context of degeneration formulas in Gromov-Witten and Donaldson-Thomas theory. We will also discuss a version of this theory in differential geometry—where manifolds with corners are the nicest objects—and explain how this is related to the algebro-geometric side of the theory.
Serge Randriambololona: Un survol de l’o-minimalité et de quelques unes de ses applications⌗
Date: October 23, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
La théorie des structures o-minimales est une généralisation de la géométrie semi-algébrique (l’étude des ensembles de $\mathbb R^n$ définis par un système fini de lieu d’annulation et de lieu de positivité de polynômes), apparue dans le milieu des années 80 dans un papier de L. van den Dries et formalisé plus tard par Pillay et Steinhorn. Elle propose une approche axiomatique de ce que peut-être une géométrie “modérée” (comme proposé par Grothendieck dans son “esquisse d’un programme”), présente de nombreux exemples naturels (une des activités importante dans le domaine constitue à établir si une théorie donnée est o-minimale ou non) et présente une souplesse qui lui permet d’établir le bon comportement de nombreux objets géométriques naturels. Je préciserai la définition d’une structure o-minimal, expliquerai les principaux théorèmes qui font qu’on la considère comme un cadre “modéré”, donnerai des exemples importants de structures o-minimales et présenterai certain de ses succès récents en théorie des nombres.
Asli Deniz: Introduction to Holomorphic Dynamics: An Extension of Holomorphic Motion⌗
Date: October 09, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
The talk consists of four sections: First, we give a short introduction to the field of holomorphic dynamics. In the second section, we introduce a specific one parameter family of transcendental entire functions. In the third part, we give a new concept termed holomorphic explosion, which we derived from holomorphic motion. The last section is devoted to an application of holomorphic explosion to the transcendental entire family in consideration.
Şükrü Yalçınkaya: Black Box Groups⌗
Date: September 25, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 09
Black box groups are introduced as an idealised setting for randomised al- gorithms for solving permutation and matrix group problems in computational group theory. A black box group G is a finite group whose elements are encoded as 0-1 strings of uniform length and the group operations are performed by an oracle (‘black box’). Given strings representing g, h in G, the black box can compute the strings representing gh, g^{-1} and decide whether g = h. In this context, a natural task is to find a probabilistic algorithm which determines the isomorphism type of a group within given (arbitrarily small) probability of error. More desirable algorithms, called constructive recognition algorithms, are the ones producing an isomorphism between a black box copy of a finite group and its natural copy. A simple observation on the recognition algorithms in black box group theory is that procedures are based on checking whether some first order formulae satisfied by the given black box group. I will focus on this observation and discuss constructive recognition of black box groups of Lie type. Along the way, I will explain how we define a standard Frobenius automorphism in a black box group isomorphic to (P)SL(2, q) and construct (or interpret) of a black box field in black box groups using only black box group operations. If time permits, I will talk about the interpretation of inverse transpose map and graph automorphisms, and the corresponding constructions in the black box groups of Lie type. This is a joint work with Alexandre Borovik.
Evrim Hilal Erdamar (Sermaye Piyasası Kurulu): Comovement between stock and bond return in Turkey.⌗
Date: May 22, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
We try to determine the relation between stock returns and changes in interest rates and attribute this relation to one of two competing hypotheses: similarity in valuation methods implying a negative relation and need for a portfolio reallocation implying a positive correlation. We find a negative correlation (-0.33), hence support the first hypothesis. However, this correlation has weakened in the period after the subprime crisis of 2007 (-0.37 vs. -0.28). Interestingly, sharp decreases in interest rates are associated with high positive correlations while sharp increases are associated with high negative correlations. This reveals an asymmetry in the relation between stock and bond returns. We also find that some sectorial indices have different sensitivities to interest rate changes.
Athanase Papadopoulos: Structure métrique de l’espace de Teichmüller⌗
Date: May 15, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Gönenç Onay: Valued Difference Fields⌗
Date: May 08, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
To a valued field one can canonically associate its residue field and value group. It is natural to ask the following question: if two valued fields have “similar” valued groups and “similar” residue fields how much are they similar as valued fields? For example, (Q_p,v_p) and (F_p((t)), v_t) have the same residue field (F_p) same and the value group (Z) and Ax-Kochen and Ershov theorem establish a “tight” similarity between this two fields that answers a conjecture of Artin. I will discuss the analogous situation where the valued fields in question are respectively equipped by distinguished automorphisms.
Evelia Garcia Barroso (Universidad de La Laguna-Tenerife): A criterion of irreducibility for complex series in two variables.⌗
Date: April 24, 2013 at 15:00
Location: Galatasaray University, FEF 10
We give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction.
Evelia Garcia Barroso (Universidad de La Laguna-Tenerife): Resolution of singularities of plane curves I-II⌗
Date: April 22, 2013 at 14:00
Location: Galatasaray University, FEF 9
(Abstract not available in text)
Burak Özbağcı: Exotic Stein fillings with arbitrary fundamental group⌗
Date: April 03, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
For any finitely presentable group G, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings whose fundamental group is isomorphic to G. Along the way, we also provide a new construction of a Lefschetz fibration over the 2-sphere whose total space has fundamental group G, using Luttinger surgery. (This is a joint work with Anar Akhmedov)
Masaaki Yoshida (Université Kyushu): 6 planes in the space⌗
Date: March 22, 2013 at 10:00
Location: Galatasaray Üniversitesi FEF 10
I will give lectures about 6 planes in the space (joint work with B. Morin): Real projective line, plane, space: definition and intuitive understanding. projective transformations. Point arrangements on the line, line arrangements on the plane, plane arrangements in the space. Six planes in the space: observation and recognition which can be very elementary.
Masaaki Yoshida: Schwarz maps for hypergeometric functions⌗
Date: March 20, 2013 at 10:30
Location: Galatasaray Üniversitesi FEF 8 - FEF 10
Review of the hypergeometric function, equation and the Schwarz map. Few comments on several high-dimensional generalizations. After these, I introduce the hyperbolic Schwarz map, whose image is a surface in the 3-dimensional hyperbolic space
Jean-Paul Brasselet (CIRM, Marseille): Orbits divisors on toric varieties.⌗
Date: March 13, 2013 at 13:30
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Jean-Paul Brasselet (CIRM, Marseille): Projective Toric Varieties.⌗
Date: March 11, 2013 at 14:00
Location: Galatasaray Üniversitesi FEF 9
(Abstract not available in text)
Thomas Hudson: An extension of Schubert polynomials for connected K-theory using algebraic cobordism.⌗
Date: January 10, 2013 at 11:00
Location: Galatasaray Üniversitesi FEF 8
Given a suitably generic morphism of vector bundles over a smooth scheme X, the Chow ring fundamental classes of the degeneracy loci can be expressed by means of the double Schubert polynomials. This result has an exact analogue in K^0(X), the Grothendieck ring of algebraic vector bundles over X, provided one replaces the double Schubert polynomials with the double Grothendieck polynomials. In this talk I will illustrate the common framework existing behind this two results and how it can be transported to algebraic cobordism, the universal oriented cohomology theory. I will also explain how this approach allows, in the universal case of a full flag bundle, to extend the result to connected K-theory, a cohomology theory that dominates both CH and K^0, leading to the definition of a family of polynomials generalizing both Schubert and Grothendieck polynomials.
2012⌗
Alp Bassa: Elliptic Curves, Drinfeld Modules and Curves over Finite Fields⌗
Date: December 26, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
In this talk I will start by introducing Elliptic Curves and their characteristic p analogues, Drinfeld Modules. I will talk about modular curves and varieties, which parametrize these objects and show how they can be used in the construction of curves over finite fields with many rational points.
Kamel Haouam: Qu’est-ce que la didactique des Mathématiques?⌗
Date: December 19, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
La didactique des mathématiques est une nouvelle science âgée de trente ans ou un peu plus, elle s’intéresse à l’étude de la transmission du savoir mathématique, en conséquence plusieurs questions se constituent à savoir: - comment le savoir s’est-il construit. - quel est le rôle de l’enseignant vis à vis de ce savoir. - suffit-il seulement de remplir les têtes vides des apprenants? On se rend compte alors qu’on est convaincu que ceci ne se réduit seulement pas à l’acquisition des contenus secs des mathématiques, c’est à partir de là que commence la didactique.
İrem Portakal: Quivers, polytopes and toric varieties⌗
Date: December 12, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
A quiver is simply an oriented graph without oriented cycles. They are frequently used to represent some of the important results in many areas of mathematics. It has shown that every quiver leads to a reflexive polytope the one we call a flow polytope. I will present a method to determine a finite list of quivers defining all d dimensional flow polytopes up to isomorphism. Also, I will describe how we can associate these purely combinatorial objects to toric varieties. One can ask if we can “understand” toric varieties by looking at its associated quiver. It still remains as an open question if one can find a criterion for smoothness of associated toric variety in terms of quiver.
Frédéric Chapoton: Combinatoire des triangulations⌗
Date: November 30, 2012 at 13:00
Location: Galatasaray Üniversitesi FEF 10
Je vais présenter plusieurs objets combinatoires remarquables (les frises de nombres, les triangulations etc.) et parler de relations parfois surprenantes entre ces différents objets. Les nombres de Catalan permettent de compter tous ces objets.
Frédéric Chapoton: Tree-indexed series⌗
Date: November 28, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Rooted trees have a rich algebraic structure, and they have been used in various domains of mathematics, including numerical analysis and renormalisation. I will present some of these algebraic structures, in particular on the vector space of tree-indexed series, which can be thought of as an analogue of formal power series. I will also describe some examples of interesting tree-indexed series.
Müge Taşkın: Tower tableaux⌗
Date: November 14, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
It is well known that any permutation w in the symmetric group Sn can be represented as the product of some finite adjacent transpositions si = (i; i + 1) where the index i runs from 1 to n - 1. Among all such representations the ones which uses the minimum number of generators are called reduced representations for w. The notion of reduced words has been catching high attention, because of their appearances in many areas that algebraic combinatorics interferes. In this talk, we introduce a new combinatorial object ”tower tableaux" together with the ”sliding algorithm" which appears as an important tool for studying reduced words in many aspects.
Vasile Berinde: Some numerical aspects of fixed point iterative methods for solving nonlinear optimization problems⌗
Date: November 05, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
(Abstract not available in text)
Stepan Orevkov: Real algebraic and real pseudoholomorphic curves⌗
Date: October 31, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Real pseudoholomorphic curves in real algebraic surfaces (in projective plane, for example) have many properties in common with real algebraic curves. If a given configuration of ovals on $RP^2$ is realizable as the set of real points of a real pseudoholomorphic curves, usually it is rather difficult to prove that it is algebraically unrealizable.In my talk,I will discuss some cases when it is nevertheless possible.
Ayşe Berkman: Characterizing Groups of Finite Morley Rank via Their Actions⌗
Date: May 29, 2012 at 15:00
Location: Galatasaray Üniversitesi FEF 10
After explaining some model theoretic concepts such as Morley rank, I shall state some characterization results of certain linear groups in the finite Morley rank context. Then I shall discuss how these results can be used in understanding generically sharp transitive actions. The talk will be accessible to graduate students.
Emel Bilgin (Univ. Essen): Classes of hypersurfaces of low degree in the Grothendick ring of varieties K_0(Var_k).⌗
Date: May 25, 2012 at 14:30
Location: Galatasaray Üniversitesi FEF9
(Abstract not available in text)
Murat Turhan (Yıldız Teknik Üniversitesi): Hirota type discretization⌗
Date: May 15, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 10
The integrable discretizations of the problems in rigid body dynamics are a vast undeveloped area of study. Certainly, the most famous ones are the three integrable cases of the rotation of a heavy rigid body around a fixed point in a homogeneous gravity field, named after Euler, Lagrange and Kowalevski. Recent studies for the integrable discrete systems show us the conspicuous relationships in unrelated areas of research such as numerical algorithms, discrete geometry, cellular automaton, quantum integrable systems and algebraic geometry tools. One of these studies, Bobenko and Suris, use Poisson construction of discretizations which gives implicit equations of motion. In this talk, we give a very different discretization method, called Hirota type discretization, using the bilinear transformation method and obtain explicit equations of motion. We give Hirota discretization of the motion of a rigid body with a fixed center of mass named Euler Top.
Nicolas Vayatis (ENS, Cachan): Statistical Learning Theory: a playground for the mathematics of prediction.⌗
Date: May 10, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 8
Les mathématiques de la prévision ont longtemps privilégié la notion de régularité locale des modèles (conditions d’existence de solutions dans les EDP, propriété des modèles statistiques garantissant la convergence des estimateurs paramétriques, etc). La théorie de l’apprentissage statistique, quant à elle, propose des concepts de nature combinatoire (complexités de Vapnik-Chervonenkis) ou géométriques (complexités de Rademacher) comme garants de la qualité des modèles à vocation prédictive. La révolution est de taille puisque cette approche récente permet d’aborder de front les questions d’inférence relatives à l’exploitation de données en grande dimension. Elle nourrit également de questionnements une communauté croissante de chercheurs confrontant informaticiens et mathématiciens issus de spécialités diverses (probabilités, statistique mathématique, géométrie convexe, optimisation) autour d’une thématique commune. L’exposé se fera l’écho des avancées récentes au sein de cette théorie aux retombées spectaculaires dans la technologie moderne.
Mihai Tibar (Univ. Lille 1, France): Betti numbers of polynomials⌗
Date: April 24, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
We explain how to initiate a classification of polynomials f from C^n to C of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may have at most one line singularity of Morse transversal type. Our method uses deformations into particular pencils with non-isolated singularities. This is a joint work with Dirk Siersma.
Haluk Şengün (University of Warwick): Cohomology of Bianchi Groups⌗
Date: April 17, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They arise naturally in the study of hyperbolic 3-manifolds and of certain generalizations of the classical modular forms (called Bianchi modular forms) for which they assume the role of the classical modular group SL(2,Z). In this latter sense, the study of Bianchi groups is fundamental for developing Langlands’ programme for GL(2) beyond totally real fields. The overall goal of this talk is to give the audience an overview of some of the fundamental problems in the arithmetic aspects of the theory of Bianchi groups. After giving the necessary background, I will start with a discussion of the problem of understanding the behavior of the dimensions of the cohomology of Bianchi groups and their congruence subgroups. Next, I will focus on the amount of the torsion that one encounters in the cohomology . Finally, I will discuss the arithmetic significance of these torsion classes.
Vincent Labatut (Université de Galatasaray): Complex Networks Analysis⌗
Date: April 10, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Networks science constitutes a very dynamic field in current research. It can be historically considered as the intersection of three preexisting domains: graph theory, complex systems analysis and data mining. Due to the great flexibility of graphs used as a modeling tool, the theoretical results obtained in network science are used in numerous applied sciences, including biology, physics, computer science, economy, human sciences, etc. In this presentation, we will first briefly describe the emergence of this relatively new field, and present its goals. We will then introduce its main concepts, and the most important results obtained in this field. We will also use a few real-world examples to illustrate what these results practically mean and show their scope. Finally, we will present the open questions currently at the center of the attention in this field.
Mark Spivakovsky (Université de Toulouse): Introduction to the problem of resolution of singularities⌗
Date: April 03, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
The aim of the talk is to give an introduction to the problem of resolution of singularities in characteristic zero and in positive characteristic (all notions required to state the problem will be defined during the talk). If time permits, we shall discuss the local version of the problem, so called “local uniformization with respect to a valuation”.
Jiro Sekiguchi (Tokyo University of Agriculture and Technology): Free Divisors and Painlevé Equations after M. Kato⌗
Date: March 20, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
First of all, I will explain the definition of free divisors and that of systems of uniformization equations with singularities along such hypersurfaces which are examples of holonomic systems. These two notions are formulated by K. Saito around 1970’s. Then I restrict my attention to the case of hypersurfaces of an affine three dimensional space. I will show some examples of free divisors in this case and uniformization equations. It turns out that the systems of uniformization equations are closely related with Painlevé equation and its algebraic solutions. Typical examples of free divisors are hypersurface defined by the discriminant of real and complex reflection groups. Recently M. Kato (Univ. of Ryukyus) clarified the relationship between systems of uniformization equations with singularities along the discriminant sets of reflection groups of rank three and algebraic solutions of Painlevé equation. In my talk I will take a survey of free divisors, uniformization equations, and discuss topics related with the results of M. Kato.
Richard Gonzales (Galatasaray University): Standard group embeddings and divided differences operators⌗
Date: March 13, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF10
Briefly speaking, a standard group embedding is a normal projective compactification of a reductive group. They can all be obtained as certain projectivizations of reductive monoids. A complete combinatorial description of the equivariant cohomology of rationally smooth embeddings (a subclass that includes smooth and certain singular varieties), has been obtained in previous work by the author. An interesting open problem is to find an explicit set of polynomial generators for the various cohomology rings thus obtained. In this introductory talk, I will provide a survey of these topics and show how Newton’s divided difference operators (and Schubert calculus) could be effectively used to solve the above-mentioned problem. This is joint work with K. Aker and Ö. Öztürk.
Dr. Ayşe Altıntaş (Yıldız Teknik Üniversitesi): Examples of finitely determined map-germs⌗
Date: February 28, 2012 at 16:00
Location: Galatasaray Üniversitesi FEF 10
The main focus of this talk will be finitely determinacy of multi valued holomorphic map-germs with respect to the Right-Left equivalence. By J. Mather’s results, finite determinacy can be characterised geometrically. An important tool for studying the geometry of maps is the notion of multiple point spaces. The k-th multiple point space of a finite map between topological spaces is the closure of the set of k-tuple points having the same image under the map and distinct components. In this talk, I shall discuss how to get algebraic criteria for finite determinacy of map-germs of any corank from 3-space to 4-space using multiple point spaces and demonstrate it with examples.
2011⌗
Bernard Teissier (Institut Mathématique de Jussieu, Equipe Géométrie et Dynamique): On the Lojasiewicz exponent⌗
Date: December 29, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
The Lojasiewicz exponent measures the relative rates of vanishing of two real or complex-analytic, or subanalytic, functions which vanish on the same set. I will survey some variations on this idea in commutative algebra, including if time permits a recent result of Moret-Bailly on the Artin-Greenberg approximation theorem.
Cemsinan Deliduman (Mimar Sinan Güzel Sanat Üniversitesi): Entanglement Swapping Model of DNA Replication⌗
Date: December 22, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
Molecular biology explains function of molecules by their geometrical and electronical structures which are mainly determined by utilization of quantum effects in chemistry. However,further quantum effects are not thought to play any significant role in the essential processes of life. On the contrary, consideration of quantum circuits/protocols and organic molecules as software and hardware of living systems that are co-optimized during evolution, may be useful to pass over the dfficulties raised by biochemical complexity and to understand the physics of life. In this talk, I will describe a quantum mechanical model of DNA replication with a reliable qubit representation of the nucleotides. In the model: 1) molecular recognition of a nucleotide is assumed to trigger an intrabase entanglement corresponding to a superposition of different tautomer forms and 2) pairing of complementary nucleotides is described by swapping intrabase entanglements with interbase entanglements. I will give some examples of quantum circuits/protocols to be used to obtain intrabase and interbase entanglements. Lastly, possible computational and experimental verification methods of the model will be discussed.
Arnaldo Garcia (IMPA at Rio de Janeiro, Sabancı Üniversitesi): Asymptotics on codes and on curves over finite fields⌗
Date: December 08, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
The famous bound of Hasse-Weil for the number of rational points on curves over finite fields (equivalent to the Riemann Hypothesis in this context) was shown by Ihara to be weaker as the genus of the curve grows. For a finite field with q elements, Ihara then introduced the quantity A(q) that controls the asymptotic behaviour of the number of rational points as the genus goes to infinity.To deal with A(q) one is led to consider infinite towers of algebraic curves and to study their limits for the ratios of (number of rational points) / (genus). We are going to motivate this interesting mathematical subject by its connection to the asymptotics in Coding Theory, which is a result due to Tsfasman-Vladut-Zink based on a construction of Goppa of linear codes from algebraic curves over finite fields.
Ayberk Zeytin (Galatasaray University): Polygonal decompositions of the sphere and ball quotients⌗
Date: November 03, 2011 at 16:00
Location: Galatasaray Üniversitesi FEF9
After a short introduction to the subject, we will give classification of sphere quadrangulations satisfying a condition of non-negative curvature, following Thurston’s classification of sphere triangulations under the same condition. If time permits, we will discuss some arithmetic applications of the classification, and its relations to Picard-Terada-Deligne-Mostow theory. (joint with M.Uludag.)
Johannes HUEBSCHMANN (Université des sciences et technologies de Lille): Singular Poisson-Kähler geometry of stratified Kähler spaces⌗
Date: May 09, 2011 at 15:30
Location: salle P20
(Abstract not available in text)
Eugene HA (Galatasaray Üniversitesi): Galois Theory from Galois’ Perspective⌗
Date: May 04, 2011 at 16:00
Location: salle FEF 8 (mercredi) et FEF 1 (jeudi)
These lectures will cover the main theorem of the Galois theory of fields following closely the original approach of Galois. We will see how Galois theory proves the nonexistence of a general algebraic formula for the roots of rational-coefficient polynomials of degree 5 or more. We shall also illustrate the general theory in the special case of cyclotomic fields and of finite fields.
Müge KANUNI (Boğaziçi Üniversitesi): Discrete Structures in Algebra⌗
Date: April 25, 2011 at 15:00
Location: salle P20
Path Algebras, Leavitt Path Algebras and Incidence Algebras are algebras defined on discrete structures. We will describe these different structures and give a brief overview of their history.
Meral TOSUN (Université Galatasaray): Good slices for simple elliptic singularities⌗
Date: April 04, 2011 at 15:00
Location: salle P20
We will first present the relation between singularities of complex surfaces and Lie algebras. Then we will show how to generalize the Slodowy slices to simple elliptic singularities.
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): Espaces métriques généralisés 2⌗
Date: March 24, 2011 at 09:00
Location: salle FEF 5
(Abstract not available in text)
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): Espaces métriques généralisés 1⌗
Date: March 23, 2011 at 16:00
Location: salle FEF 10
(Abstract not available in text)
Jiro SEKIGUCHI (Tokyo University of Agriculture and Technology): A Schwarz map of Appell’s F_2 whose monodoromy group is related to the reflection group of type D_4⌗
Date: March 21, 2011 at 16:00
Location: salle FEF 7
The system of differential equations for Appell’s hypergeometric function F_2(a,b,b’,c,c’;x,y) has four fundamental solutions. Let u_1,u_2,u_3,u_4 be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y)) is a hypersurface S of the 3-dimensional projective space {\bf P}$. Then S is defined by P(u_1,u_2,u_3,u_4)=0 for a polynomial P(t_1,t_2,t_3,t_4). It is M. Kato (Univ. Ryukyus) who determined the parameter a,b,b’,c,c’ such that the monodromy group of the system for F_2(a,b,b’,c,c’;x,y) is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group G of rank four by an abelian group. In this talk, we treat the system for F_2(a,b,b’,c,c’;x,y) with (a,b,b’,c,c’)=(1/2,1/6,-1/6,1/3,2/3. In this case, the monodromy group is the semidirect group of G by Z/3Z, where G is the reflection group of type D_4. The polynomial P(t_1,t_2,t_3,t_4) in this case is of degree four. There are 16 ordinary singular points in the hypersurface S. In the rest of my talk, I explain the background of the study.
Athanase PAPADOPOULOS (Institut de Recherche Mathématique Avancée, Strasbourg): La géométrie de Finsler⌗
Date: March 21, 2011 at 15:00
Location: salle FEF 7
(Abstract not available in text)
Eric SOCCORSI (centre de physique théorique, Marseille): Résolution des équations différentielles par la méthode des élements finis⌗
Date: March 16, 2011 at 15:00
Location: salle FEF 9
J’expliquerai comment on résout “numériquement” une EDP en prenant pour simplifier un exemple d’EDO.
Eric SOCCORSI (centre de physique théorique, Marseille): Lipschitz stability in an inverse problem for non autonomous magnetic Schrödinger equations⌗
Date: March 14, 2011 at 16:00
Location: salle FEF 7
We consider the inverse problem of determining the time dependent magnetic field of the Schrödinger equation in a bounded open subset of R^n, n>=1, from a finite number of Neumann data, when the boundary measurement is taken on an appropriate open subset of the boundary. We prove the Lispchitz stability of the magnetic potential in the Coulomb gauge class by n times changing initial value suitably.
Oleg BELEGRADEK (İstanbul Bilgi Üniversitesi): How similar can non-isomorphic algebraic structures be?⌗
Date: March 14, 2011 at 15:00
Location: salle FEF 7
In this talk (oriented to a general mathematical audience not necessarily familiar with model theory) I will discuss the notion of elementary equivalence, one of the basic notions of model theory, illustrating it with various algebraic examples, both classical and more recent. In particular, some author’s results on model-theoretic properties of unitriangular groups will be discussed.
Jawad SNOUSSI (Universidad Nacional Autónoma de México): Modifiactions des singularités⌗
Date: March 09, 2011 at 15:00
Location: salle FEF 10
Nous expliquerons les concepts d’éclatement, de normalisation, de modification de Nash et leur relations avec la résolution des singularités
Jawad SNOUSSI (Universidad Nacional Autónoma de México): Equisingularity in complex surfaces⌗
Date: March 07, 2011 at 15:00
Location: salle FEF 4
We explain the equivalence for complex surfaces between Whitney regularity and Zariski equisingularity criterion. We will give some applications such as the fact that any surface Whitney regular along its singular locus has a smooth normalisation.
Eugene HA (Université Galatasaray & Fields Institute, Toronto): The problem of cohomology for an Arakelov divisor⌗
Date: February 28, 2011 at 15:00
Location: salle P 23
We shall discuss Tate’s Riemann-Roch theorem for number fields and the peculiar nature that it implies for the cohomology of an Arakelov divisor (that is, a divisor for the spectrum of a number field formally completed at archimedean infinity).
Gülay KAYA (Université Galatasaray): The Groebner fan of a polynomial ideal⌗
Date: January 07, 2011 at 15:00
Location: salle FEF 1
(Abstract not available in text)
2010⌗
Muhammed ULUDAĞ (Université Galatasaray): Hypergeometric Galois Actions⌗
Date: December 20, 2010 at 15:00
Location: salle FEF 9
(Abstract not available in text)
Cédric MILLIET (Université Galatasaray): Quelques mots de théorie des modèles⌗
Date: December 06, 2010 at 15:00
Location: salle FEF 9
Le but de l’exposé est de faire voir un peu de théorie des modèles. J’ai choisi de présenter un théorème de Macintyre (de 1971) disant qu’un corps omega-stable est soit fini, soit algébriquement clos. Après avoir dit ce qu’est une théorie, ou un modèle, et énoncé quelques questions typiques que se posent habituellement les logiciens, je rappelerai deux invariants des espaces topologiques compacts dénombrables qui permettent de les classifier à homéomorphisme près, avant de donner une preuve du théorème de Macintyre, allégée grâce à des arguments de Poizat. L’exposé devrait être accessible à tous.
Susumu TANABE (Université Galatasaray): Invariants of hypergeometric groups for Calabi–Yau complete intersections in weighted projective spaces⌗
Date: November 24, 2010 at 17:15
Location: salle FEF 9
Let Y be a smooth Calabi–Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the mirror manifold of Y in the sense of Batyrev and Borisov is one-dimensional and spanned by the Gram matrix of a classical generator of the derived category of coherent sheaves on Y with respect to the Euler form. This is a confirmation of an expected consequence of the homological mirror symmetry conjecture by Kontsevitch.
Xavier BRESSAUD (Institut de Mathématiques de Toulouse): Introduction à la dynamique symbolique. (2/2)⌗
Date: November 05, 2010 at 10:00
Location: salle P 19
(Abstract not available in text)
Xavier BRESSAUD (Institut de Mathématiques de Toulouse): Introduction à la dynamique symbolique. (1/2)⌗
Date: November 04, 2010 at 10:00
Location: salle FEF 9
(Abstract not available in text)
Hervé GAUSSIER (Institut Joseph Fourier, Grenoble): Pseudoholomorphic curves and applications⌗
Date: October 27, 2010 at 16:00
Location: salle FEF 10
Pseudoholomorphic curves are important objects by their role in different subjects such as symplectic or contact geometry. I will present recent results on the study of almost complex manifolds, concerning the (non)existence of pseudoholomorphic curves and more generally of pseudoholomorphic maps.
Hervé GAUSSIER (Institut Joseph Fourier, Grenoble): Géométrie et calcul infinitésimal. Séminaire introductif à destination des étudiants⌗
Date: October 26, 2010 at 15:00
Location: salle FEF 1
J’essaierai de montrer les liens entre la géométrie classique, notamment la construction à la règle et au compas, et les premières études sur le calcul différentiel. Je montrerai aussi l’évolution de la géométrie euclidienne vers d’autres géométries.
Colloquium⌗
2017⌗
Romanian-Turkish Mathematics Colloquium II⌗
Date: October 25, 2017 at 09:00
Location: Galatasaray University
Second Romanian-Turkish Mathematics Colloquium - joint meeting. More info: https://math.gsu.edu.tr/2017RT.html
Workshop / Meeting⌗
2024⌗
AGCCA (Algebraic Geometry, Computational Commutative Algebra)⌗
Date: June 20, 2024 at 09:00
Location: Galatasaray University
Workshop on Algebraic Geometry and Computational Commutative Algebra. More info: https://math.gsu.edu.tr/agcca/agcca.html
Trustworthy AI Workshop⌗
Date: March 29, 2024 at 09:00
Location: Galatasaray University
Workshop on Trustworthy AI. More info: https://math.gsu.edu.tr/trustworthyAI.html
2023⌗
Teichmüller Theory Workshop (Adana)⌗
Date: February 03, 2023 at 09:00
Location: Adana
Workshop on Teichmüller Theory. More info: https://math.gsu.edu.tr/adanaTM.html
2020⌗
Monodromy and Hypergeometric Functions Workshop⌗
Date: February 17, 2020 at 09:00
Location: Galatasaray University
Workshop on Monodromy and Hypergeometric Functions. More info: https://math.gsu.edu.tr/2020workshopmonodhypergeom.html
2018⌗
Mathematical Topics in Quantization Workshop⌗
Date: September 12, 2018 at 09:00
Location: Galatasaray University
Workshop on Mathematical Topics in Quantization. More info: https://math.gsu.edu.tr/2018workshopgeomquant.html
2017⌗
Tropical Geometry in Istanbul⌗
Date: January 15, 2017 at 09:00
Location: Istanbul
Workshop on Tropical Geometry. Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
2016⌗
Extended Differential Calculus Workshop⌗
Date: June 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Extended Differential Calculus. More info: https://math.gsu.edu.tr/diff2016
Arithmetic and Low Dimensional Hyperbolic Spaces Workshop⌗
Date: June 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Arithmetic and Low Dimensional Hyperbolic Spaces. More info: https://math.gsu.edu.tr/2016ahslow.html
Algebra, Geometry and Topology of Singularities Workshop⌗
Date: May 15, 2016 at 09:00
Location: Galatasaray University
Workshop on Algebra, Geometry and Topology of Singularities. More info: https://math.gsu.edu.tr/singularities2016/
2013⌗
Japanese-Turkish Joint Geometry Meeting⌗
Date: November 21, 2013 at 09:00
Location: Galatasaray University
Japanese-Turkish Joint Geometry Meeting. More info: https://math.gsu.edu.tr/2013jpn-tr.html
MSGSU-GSU Toric and Tropical Geometry Meetings⌗
Date: September 15, 2013 at 09:00
Location: Galatasaray University / Mimar Sinan Güzel Sanatlar Üniversitesi
Recurring weekly meetings on Toric and Tropical Geometry (2013). More info: https://istanbulttgmeetings.wordpress.com
İstanbul Number Theory Meetings II⌗
Date: March 16, 2013 at 09:00
Location: Galatasaray University (Barlas Tolan)
Meeting featuring talks on o-minimal structures and number theory, including ‘A Fast Introduction to O-minimality’ and applications of the Pila-Wilkie counting theorem (Manin-Mumford conjecture). More info: https://math.gsu.edu.tr/2013intm-8.html
İstanbul Number Theory Meetings I⌗
Date: February 16, 2013 at 09:00
Location: IMBM, Istanbul
Meeting featuring four speakers from Istanbul universities discussing automated theorem proving, subgroups of infinite dihedral groups, binary quadratic forms, and Thompson’s groups. More info: https://math.gsu.edu.tr/2013intm.html
2012⌗
İstanbul Workshop on Teichmüller Theory⌗
Date: October 11, 2012 at 09:00
Location: Istanbul
İstanbul Workshop on Teichmüller Theory. More info: https://math.gsu.edu.tr/2012iwtt.html
İstanbul Workshop on Fixed Point Theory and Applications⌗
Date: October 11, 2012 at 09:00
Location: Galatasaray University
International workshop (11-14 October 2012) on fixed point theory with emphasis on applications in natural sciences, economics, finance, computing, and engineering. More info: https://math.gsu.edu.tr/2012iwfpta.html
ICTB Workshop on Recent Trends in Algebraic Number Theory⌗
Date: June 15, 2012 at 09:00
Location: Galatasaray University
ICTB Workshop on Recent Trends in Algebraic Number Theory (June 2012). Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
CIMPA Meeting on Regional Cooperation⌗
Date: June 15, 2012 at 09:00
Location: Galatasaray University
CIMPA meeting on regional cooperation (June 2012). Listed on https://matematik.gsu.edu.tr/tr/arastirma/calistaylar-konferanslar
Conference⌗
2026⌗
Visite de Salah Mehdi, Université de Lorraine⌗
Date: March 23, 2026
Visite de Cedric Villani⌗
Date: March 23, 2026
2025⌗
Visiteur: Arnaud Bodin, Université de Lille⌗
Date: February 19, 2025
2024⌗
Visiteur: Didier Lesevre, Université de Lille⌗
Date: November 25, 2024
2022⌗
Athanase Papadopoulos 65th Birthday Conference⌗
Date: June 20, 2022 at 09:00
Location: Galatasaray University
Conference celebrating Athanase Papadopoulos’s 65th Birthday. More info: https://math.gsu.edu.tr/websitesiathanpapa.html
2019⌗
Journées Arithmétiques 2019⌗
Date: July 01, 2019 at 09:00
Location: Istanbul
Journées Arithmétiques international conference. More info: https://math.gsu.edu.tr/JA2019.html
2015⌗
Fixed Point Theory and Its Applications⌗
Date: July 01, 2015 at 09:00
Location: Galatasaray University
Conference (July 2015) bringing together experts in fixed point theory, with emphasis on applications across natural sciences, medicine, economics, and engineering. More info: https://math.gsu.edu.tr/fixed-point-theory.html
2014⌗
Finsler Geometry and Applications Conference⌗
Date: April 10, 2014 at 09:00
Location: Galatasaray University
Conference on Finsler Geometry and Applications. More info: https://math.gsu.edu.tr/2014-finsler.html
Japanese-Turkish Joint Geometry Conference II⌗
Date: March 19, 2014 at 09:00
Location: Galatasaray University
Second Japanese-Turkish Joint Geometry Conference. More info: https://math.gsu.edu.tr/2014-geometry.html
2011⌗
Geometry and Arithmetic around Teichmüller Theory Conference⌗
Date: November 15, 2011 at 09:00
Location: Galatasaray University
Conference on Geometry and Arithmetic around Teichmüller Theory. More info: https://math.gsu.edu.tr/2011gatt.html
Summer School / Course⌗
2026⌗
Mini Cours - Salah Mehdi, Université de Lorraine⌗
Date: March 26, 2026 at 08:00
A Matrix Centered Introduction to Lie Groups and Lie Algebras - Part 2
Mini Cours - Salah Mehdi, Université de Lorraine⌗
Date: March 24, 2026 at 12:00
A Matrix Centered Introduction to Lie Groups and Lie Algebras - Part 1
2025⌗
Mini cours: Mathématiques pour ChatGPT et les réseaux de neurones - Arnaud Bodin, Univ. de Lille⌗
Date: February 27, 2025 at 13:00
Mini cours: Mathématiques pour ChatGPT et les réseaux de neurones - Arnaud Bodin, Univ. de Lille⌗
Date: February 26, 2025 at 13:00
2024⌗
René Cori (Institut de Mathématiques de Jussieu-Paris Rive Gauche): Undecidable mathematical statements⌗
Date: December 11, 2024 at 12:00
Location: Galatasaray Üniversitesi, Room H306
We all know that in Mathematics, there are statements that can neither be proved nor disproved, such as the axiom of choice or the continuum hypothesis. We also sometimes hear about statements that are “true” but “not provable”. But what does all this mean? Are such statements unavoidable? The notion of “model of set theory” helps clarifying these issues. Of course, we need to specify the meaning of “proving”! Starting with elementary facts about groups, we shall explain what a complete theory is and why Mathematics is hopelessly incomplete.
Mini cours: Formes Modulaires et Formule de Trace de Peterson - Didier Lesevre, Univ. de Lille⌗
Date: November 26, 2024 at 06:00
Mini cours: Formes Modulaires et Formule de Trace de Peterson - Didier Lesevre, Univ. de Lille⌗
Date: November 25, 2024 at 08:00
2019⌗
Mini School on Singularities of Surfaces⌗
Date: November 06, 2019 at 09:00
Location: Galatasaray University
Mini School on Singularities of Surfaces. More info: https://math.gsu.edu.tr/Nov2019.html
2017⌗
Mini Cours: Topologie des singularités réelles⌗
Date: June 06, 2017 at 09:00
Location: Galatasaray University
Mini course (6-7-8 June 2017) on topology of real singularities.
Mini Cours: Les Espaces des Arcs et Résolution des Singularités⌗
Date: June 06, 2017 at 09:00
Location: Galatasaray University
Mini course (6-7-8 June 2017) on arc spaces and resolution of singularities.
2016⌗
A Short Course in Diffeology⌗
Date: November 23, 2016 at 09:00
Location: Galatasaray University
Short course in Diffeology (23-24-25-28-30 November, 1 December 2016). More info: https://math.gsu.edu.tr/documents/Programme%20Diffeology%20Oct-Nov%202016.pdf
Lecture Series on Various Aspects of Number Theory⌗
Date: March 05, 2016 at 09:00
Location: IMBM, Istanbul (in collaboration with Galatasaray University)
Lecture series (5-19 March 2016) on various aspects of number theory, with introductory parts accessible to graduate students and non-specialists. More info: https://math.gsu.edu.tr/2016IMBMWorkshop.html
Patrick Iglesias-Zemmour: Diffeology Course (Patrick Iglesias-Zemmour)⌗
Date: March 01, 2016 at 09:00
Location: Galatasaray University
Course on Diffeology by Patrick Iglesias-Zemmour. More info: https://math.gsu.edu.tr/documents/Programme%20Diffeology.pdf
2015⌗
Jiro Sekiguchi: A generalization of Okubo type differential equations and flat structures⌗
Date: March 27, 2015 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Flat structures are formulated by K. Saito in the course of the study of moduli spaces of isolated singularities. The purpose of this talk is to introduce the notion of flat structures without potentials, formulate one of generalisations of ordinary differential equations of Okubo type to several variables case and give examples of potential vector fields related with algebraic solutions of Painlev'e VI, free divisors arising from 1-parameter deformations of singularities on plane curves and discriminants of complex reflection groups. This is a joint work with M. Kato and T. Mano of University of Ryukyus.
2014⌗
CIMPA/TÜBİTAK Summer School: Algebraic Geometry & Number Theory⌗
Date: June 02, 2014 at 09:00
Location: Galatasaray University
CIMPA/TÜBİTAK Summer School on Algebraic Geometry and Number Theory. More info: https://math.gsu.edu.tr/2014agnt.html
Ian Morrison: Geometric Invariant Theory and its Applications to Moduli⌗
Date: April 25, 2014 at 09:00
Location: Galatasaray Üniversitesi, FEF 10
Lecture series by Ian Morrison (25 April – 21 May 2014) on Basic Notions of Invariant Theory and Its Applications to Moduli. More info: https://math.gsu.edu.tr/morrison-invariant.html
2013⌗
Refik Arkut: Internet, Karmaşıklık, MOOC ve Gelecekte Eğitim.⌗
Date: February 27, 2013 at 15:00
Location: Galatasaray Üniversitesi FEF 10
Bu seminerde konuşmacı kendi kişisel deneyimlerini, Internet’in başlangıç noktasından başlayarak anlatacak ve karmaşıklık kuramı ile ilk tanışmasının verdiği merakla, öğrenme dürtüsünün kendisini getirdiği MOOC (Massively On-line Open Course)’taki son ‘öğrencilik’ macerasına değinecektir. Henüz emekleme çağındaki Internet’in bize gelecekte neler sunabileceği konusunuda öngörülerini ‘Gelecekte Eğitim’ örneği ile tartışacaktır. Seminerde SFI (Santa Fe Institute) düzenlenen (on-line) ‘Introduction to Complexity’ dersinden bazı örnekler sunulacaktır.
2011⌗
Fonktörsellik ve Eşleşme (Functoriality Short Course)⌗
Date: March 30, 2011 at 09:00
Location: Galatasaray Üniversitesi
Intensive short course (30 March – 27 April 2011) featuring Robert Langlands and other mathematicians on functoriality, reciprocity principles, L-functions, trace formulas, and geometric approaches. More info: https://math.gsu.edu.tr/fonktorsellik.html
2010⌗
CIMPA/TÜBİTAK Summer School: Commutative Algebra & Applications⌗
Date: September 12, 2010 at 09:00
Location: Galatasaray University
CIMPA/TÜBİTAK Summer School on Commutative Algebra and Applications. More info: https://math.gsu.edu.tr/2010/
2009⌗
GTEM/TÜBİTAK Summer School: Geometry & Arithmetic around Galois Theory⌗
Date: June 08, 2009 at 09:00
Location: Galatasaray University
GTEM/TÜBİTAK Summer School on Geometry and Arithmetic around Galois Theory. More info: https://math.gsu.edu.tr/GAGT/
2008⌗
GTEM/TÜBİTAK Summer School: Moduli Spaces of Coverings⌗
Date: June 09, 2008 at 09:00
Location: Galatasaray University
GTEM/TÜBİTAK Summer School on Moduli Spaces of Coverings. More info: https://math.gsu.edu.tr/GAMSC/
2007⌗
CIMPA Summer School: Arrangements, Local Systems & Singularities⌗
Date: June 11, 2007 at 09:00
Location: Galatasaray University
CIMPA Summer School on Arrangements, Local Systems and Singularities. More info: https://math.gsu.edu.tr/als/
2006⌗
EMS Summer School: Arithmetic & Geometry Around Quantization⌗
Date: June 05, 2006 at 09:00
Location: Galatasaray University
EMS Summer School on Arithmetic and Geometry Around Quantization. More info: https://math.gsu.edu.tr/agaq/
2005⌗
CIMPA Summer School: Arithmetic & Geometry Around Hypergeometric Functions⌗
Date: June 13, 2005 at 09:00
Location: Galatasaray University
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions. More info: https://math.gsu.edu.tr/agahf/
Festival / Outreach⌗
2019⌗
İstanbul Matematik Festivali 2019⌗
Date: May 04, 2019 at 09:00
Location: Istanbul
İstanbul Mathematics Festival - outreach event for students and public. More info: https://math.gsu.edu.tr/festival2019
Last updated: May 27, 2026 at 11:52