Besides research projects and seminars on special topics, weekly colloquium talks are organized since the foundation of the department.

Lieu/yer: Galatasaray Üniversitesi, room I222.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Exploring the frontier of mathematical reasoning with large language models

Özet/Résumé/Abstract: 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.

Lieu/yer: Galatasaray Üniversitesi, room I204.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: On Domination Number of Cayley Graphs

Özet/Résumé/Abstract: A dominating set of Γ 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 γ(Γ) is the minimum cardinality of a dominating set for Γ. An efficient dominating set of Γ 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 Γ, then D is also minimum dominating set of Γ. 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.

Lieu/yer: Galatasaray Üniversitesi, room I109.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Optimal maps between surfaces

Özet/Résumé/Abstract: 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.

Lieu/yer: Galatasaray Üniversitesi, room I204.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: How do fluids behave, numerical modelling, new fronts, and applications

Özet/Résumé/Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room I204.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Seismic Wave Propagation and Representation of Seismic Sources

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room I204.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Data-driven learning of Lie groups

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Data-driven learning of Lie groups

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Singular foliations and Lie \(\infty\)-algebroids

Özet/Résumé/ Abstract: 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 \(\infty\)-algebroid structure on this resolution. The choices entering the construction of this Lie \(\infty\)-algebroid, including the chosen underlying resolution, are unique up to homotopy and, moreover, every other Lie \(\infty\)-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 \(\infty\)-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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Singularities and Rearrangement of Knots Via (Co)amoebas

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: From Fourier series to asymptotics of characters : a glimpse into Lie theory

Özet/Résumé/ Abstract: 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 Pandži´c, David Vogan and Roger Zierau.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Algebraic Curves, Computer Algebra and Integrable Systems

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: On the Casas–Alvero conjecture

Özet/Résumé/ Abstract: Let \(k\) be a field, \(d\) a strictly positive integer and \(x\) an independent variable. Let \(f \in k[x]\) be a monic polynomial of degree \(d\). For \(i \in \{1, \dots , d - 1 \}\), let \(f^{(i)}\) denote the \(i\)-th derivative of \(f\) (the \(i\)-th Hasse derivative in case char \(k > 0\)). Assume that for all \(i \in \{1, \dots , d - 1 \}\) the polynomial \(f^{(i)}\) has a non-trivial common factor with \(f\). The Casas–Alvero conjecture asserts that, assuming char \(k = 0\), there exists \(a \in k\) such that \(f(x) = (x - a)^d\). If char\((k) = p > 0\), the conjecture is false in general. Let us write \(\text{CA}_{d,p}\) 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 \(d\): \(\text{CA}_{d,0}\) holds \(\iff \text{CA}_{d,p}\)holds for some prime number \(p \iff \text{CA}_{d,p}\) holds for all but finitely many primes \(p\). A prime number \(p\) is said to be a bad prime for \(d\) if \(\text{CA}_{d,p}\) 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 \(dp^l\), 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 \(d\).

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: A theoretical and computational framework for upscaling epithelial subcellular dynamics to tissue mechanics

Özet/Résumé/ Abstract: 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.

Lieu/yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Indices of vector fields for mixed singularities

Özet/Résumé/Abstract: A mixed function is a real analytic function \(f\colon\mathbb{C}^n\to\mathbb{C}\) in the complex variables \(z_1,\dots,z_n\) and their conjugates \(\bar{z}_1,\dots,\bar{z}_n\). In this talk we define an integer valued index for vector fields \(v\) with isolated singularity at \(\mathbf{0}\) on real analytic varieties \(V_f:=f^{-1}(0)\) defined by mixed functions \(f\) with isolated critical point at \(\mathbf{0}\). We call this index the

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Polynomial Real Root Certification using Hermite Matrices over Q

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: On a special family cyclic codes and their applications

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: Nonlocal Vibration Analysis of 3-D Plates Using Riesz-Caputo Fractional Derivative.

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest: TBA.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: TBAŞafak Özden

Özet/Résumé/ Abstract: TBA

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

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Özet/Résumé/ Abstract: TBA

Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

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Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

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Lieu /yer: Galatasaray Üniversitesi, room H304.

Konuşmacı/Invité/Guest:

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Lieu /yer: Galatasaray Üniversitesi, room A324.

Konuşmacı/Invité/Guest: Can Ozan Oğuz, Gebze Technical University Institute of Information Technologies

Başlık/Titre/Title: Induction and restriction on symmetry groups of binary trees

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room A324.

Konuşmacı/Invité/Guest: Gönenç Onay

Özet/Résumé/ Abstract: You can find the abstract here.

Lieu /yer: Galatasaray Üniversitesi, room A324.

Konuşmacı/Invité/Guest: Özlem Ejder, Boğaziçi University

Başlık/Titre/Title: Isolated points on Modular Curves

Özet/Résumé/ Abstract: 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

Lieu /yer: Microsoft Teams (to get the link for the talk, please send a mail to ozgeulkem@gmail.com)

Konuşmacı/Invité/Guest: Türkü Özlüm Çelik, Boğaziçi University

Başlık/Titre/Title: Algebraic Curves to their Jacobians and back (You can find the slides of the talk here)

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray University, room A324

Konuşmacı/Invité/Guest: Ahmad Rafiqi, Galatasaray University

Başlık/Titre/Title: Characterizing Abelian differentials and pseudo-Anosov maps as permutations of integers (You can find the slides of the talk here)

Özet/Résumé/ Abstract: 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.

Lieu /yer: Galatasaray Üniversitesi, room H306

Konuşmacı/Invité/Guest: Fatma Çiçek

Özet/Résumé/ Abstract: You can find the abstract here.

Lieu /yer: Galatasaray Üniversitesi, room H306

Konuşmacı/Invité/Guest: Zehra Bilgin, Fatih Sultan Mehmet Vakıf University

Özet/Résumé/ Abstract: You can find the title and abstract here. (You can find the slides of the talk here)

Lieu /yer: Galatasaray University, room H306

Konuşmacı/Invité/Guest: Ezgi Kantarcı Oğuz , Boğaziçi University

Başlık/Titre/Title: Rank Polynomials of Fence Posets are Unimodal (You can find the slides of the talk here)

Özet/Résumé/ Abstract: 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).

Lieu /yer: Microsoft Teams (to get the link for the talk, please send a mail to ozgeulkem@gmail.com)

Konuşmacı/Invité/Guest: Hatice Boylan , Istanbul University

Başlık/Titre/Title: The sum of all natural numbers, prime numbers and other mysteries

Özet/Résumé/ Abstract: 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.

Lieu /yer: Microsoft Teams (to get the link for the talk, please send a mail to ozgeulkem@gmail.com)

Konuşmacı/Invité/Guest: Kevin Buzzard , Imperial College London

Başlık/Titre/Title: Teaching proofs to a computer (You can find the slides of the talk here)

Özet/Résumé/ Abstract: 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.

Lieu /yer: TBA

Konuşmacı/Invité/Guest: Yasemin Kara , Boğaziçi University

Başlık/Titre/Title: Solving Fermat Type Equations Via Modular Approach

Özet/Résumé/ Abstract: 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.

Lieu /yer: TBA

Konuşmacı/Invité/Guest: Asgar Jamneshan , Koç University

Başlık/Titre/Title: The structure of arbitrary Conze-Lesigne systems(You can find the slides of the talk here)

Özet/Résumé/ Abstract: 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.

**2018-2019 (Organized by Alexis Michel)**

Gün/Date: 08 Mai (Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi I219.

Konuşmacı/Invité/Guest : Nigar Tuncer, Bilgi University, İstanbul:

Başlık/Titre/Title: The Principles of Topofold: designed modular biomolecular folds

Özet/Résumé/ Abstract

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.

Gün/Date: 19 Avril (Vendredi) 10:00

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 8.

Konuşmacı/Invité/Guest : José Cidade Mourao, Professeur, Instituto Superior Tecnico,
Lisbon:

Başlık/Titre/Title: Complex Symplectomorphisms, Kahler Geodesics and Representation Theory.

Özet/Résumé/ Abstract

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.

Gün/Date: 10 Avril (Mercredi) 15:30

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 8 .

Konuşmacı/Invité/Guest : Lorenzo Ramero, Professeur, Laboratoire de mathématiques Paul
Painlevé, Université de Lille:

Başlık/Titre/Title: Les presques anneaux.

Özet/Résumé/ Abstract

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.

Gün/Date: 10 Avril (Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi I219.

Konuşmacı/Invité/Guest : Pierrette Cassou-Noguès, Professeure émérite, Institut de
Mathématiques de Bordeaux, Université de Bordeaux:

Başlık/Titre/Title: Structure de l'arbre à l'infini d'un polynôme à deux variables. (travail commun avec Daniel Daigle, Université de Ottawa)

Özet/Résumé/ Abstract

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.

Gün/Date: 20 Mars (Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi I219 (à verifier).

Konuşmacı/Invité/Guest : Hakan Ayral - Galatasaray Üniversitesi:

Başlık/Titre/Title: Convolutional, Recurrent and Deep Neural Networks

Özet/Résumé/ Abstract

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.

Gün/Date: 06 Mars (Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi I219.

Konuşmacı/Invité/Guest : Camille Plénat - l'Institut de Mathématiques de Marseille, Aix
Marseille Université:

Başlık/Titre/Title: Toric embedded resolutions of simple singularities via jet schemes.

Özet/Résumé/ Abstract

(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.

Gün/Date: 27 Février(Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Mohammad Sadek - Sabancı University:

Başlık/Titre/Title: How long can a curve capture a sequence?

Özet/Résumé/ Abstract

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.

You can find the abstract as a pdf file
here.

Gün/Date: 06 Février(Mercredi) 14:00

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Mee Seong Im - United States Military Academy, West Point, NY:

Başlık/Titre/Title: Almost-commuting varieties with a flag,

Özet/Résumé/ Abstract

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.

Gün/Date: 19 Décembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Hironori SHIGA - Chiba university:

Başlık/Titre/Title: A K3 modular function induced from a simple K3 singularity,

Özet/Résumé/ Abstract

You can find the abstract
here.

Gün/Date: 19 Décembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Nermine El Sissi - The American University in Cairo:

Başlık/Titre/Title: A Combinatorial Interpretation of the LDU-Decomposition of Totally Positive Matrices and their Inverses,

Özet/Résumé/ Abstract

You can find the abstract
here.

Gün/Date: 12 Décembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Bruno Deschamps, Université du Mans:

Başlık/Titre/Title: Regarding a weak inverse Galois problem

Özet/Résumé/ Abstract

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.

Gün/Date: 28 Novembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Mehmet Akif Erdal, Université Bilkent:

Başlık/Titre/Title: Realizability of vector bundles by normal bundles of manifolds

Özet/Résumé/ Abstract

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.

Gün/Date: 21 Novembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Can Ozan Oğuz, Galatasaray Universitesi

Başlık/Titre/Title: Categorification and Heisenberg algebras

Özet/Résumé/ Abstract

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 .

Gün/Date: 7 Novembre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : Ezgi Kantarci, Galatasaray Universitesi

Başlık/Titre/Title: A Queer Crystal Structure on Shifted Tableaux

Özet/Résumé/ Abstract

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.

Gün/Date: 24 Octobre(Mercredi)

Yer/Lieu/Place: Galatasaray Üniversitesi FEF 10.

Konuşmacı/Invité/Guest : François Apery, Université de Haute Alsace

Başlık/Titre/Title: On an algebraic definition of the Boy surface

Özet/Résumé/ Abstract

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.

Date/ gün: 10 Octobre(Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Muhammed Uludağ

Titre/Başlık: Mapping Class Groupoids, Thompson’s groups and Outer Automorphism Groups of Free Groups

Abstract/ Özet:

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.

**2017-2018 (Organized by Buse Fırat)**

Date/ gün: 2 May(Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Ozlem Beyarslan

Titre/Başlık: Fields with Virtually Free Group Action

Abstract/ Özet:

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.

Date/ gün: 25 April(Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Hussein Mourtada

Titre/Başlık: Arc spaces and partition identities

Abstract/ Özet:

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.

Date/ gün: 11 April(Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Michel Coornaert

Titre/Başlık: The Garden of Eden theorem: from Conway's Game of Life to Arnold's cat

Abstract/ Özet:

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.

Date/ gün: 4 April(Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Ipek Tuvay

Titre/Başlık: Stable equivalence of Morita type and Scott modules

Abstract/ Özet:

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.

Date/ gün: 21 March (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Valentin Burcea

Titre/Başlık: Formal Holomorphic Embeddings Between BSD-Models

Abstract/ Özet:

I will be talking about the classification problem for Formal Holomorphic Embeddings between
Shilov Boundaries of Bounded and Symmetric Domains.

Date/ gün: 7 March (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 7.

Conférencier/ konuşmacı: Mohan Ravichanran

Titre/Başlık: Finite free probability

Abstract/ Özet:

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.

Date/ gün: 27 December (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Atabey Kaygun

Titre/Başlık: Distributive Laws and Unramified Graph Coverings

Abstract/ Özet:

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.

Date/ gün: 13 December (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: İlker Savaş Yüce

Titre/Başlık:Isometries of length 1 in purely loxodromic free Kleinian groups and trace inequalities

Date/ gün: 6 December (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Hakan Güntürkün

Titre/Başlık: Some Results On Line Arrangements

Abstract/ Özet:

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.

Date/ gün: 29 November (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Nihat Berker

Titre/Başlık: Chateaubriand, Simone de Beauvoir, MIT, and Augmented Mechanics: Education and Research across 3 Cultures

Date/ gün: 15 November (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Jean-Louis Verger-Gaugry

Titre/Başlık: Limit Problems in Number Theory, Lehmer's Conjecture and Dynamical Zeta Functions

Abstract/ Özet:

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.

Date/ gün: 8 November (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: İlhan İkeda

Titre/Başlık: On the Langlands functoriality principle

Abstract/ Özet:

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.

Date/ gün: 7 Juin (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Nicolas Dutertre

Titre/ Lispchitz-Killing curvatures of semi-algebraic sets

Abstract/ Özet:

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.

Date/ gün: 17 Mai (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Can Deha Karıksız

Titre/ Hypercyclicity of Weighted Backward Shifts on Spaces of Real Analytic Functions

Abstract/ Özet:

Abstract

Date/ gün: 03 Mai (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Roland Bacher

Titre/ How to poison all the big rats

Abstract/ Özet:

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).

Date/ gün: 03 Mai (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Enver Özdemir

Titre/ Class number of Real Quadratic Fields

Abstract/ Özet:

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.

Date/ gün: 26 Avril (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Mustafa Topkara

Titre/ Decomposability of Fiber Bundles

Abstract/ Özet:

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.

Date/ gün: 19 Avril (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Oğul Esen

Titre/ Matching of dynamical systems: With an introduction to Geometric Mechanics

Abstract/ Özet:

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.

Date/ gün: 15 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Denis Ibadula

Titre/ Techniques for computing the Igusa local zeta function of some plain curves

Abstract/ Özet:

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.

Date/ gün: 8 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Esengül Saltürk

Titre/ Self-Dual Codes Over Local Frobenius Rings

Abstract/ Özet:

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.

Date/ gün: 30 November (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Murad Özaydın

Titre/ Noncommutative Algebraic Geometry on a Leavitt Path Algebra of Polynomial Growth

Abstract/ Özet:

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.

Date/ gün: 23 November (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Ayten Koç

Titre/ Simple Modules of Leavitt Path Algebras of Polynomial Growth

Abstract/ Özet:

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.

Date/ gün: 16 Novembre (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Zehra Balli

Titre/ Comparaison Numérique Eléments Finis et Méthode Isogeometrique

Abstract/ Özet:

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).

Date/ gün: 26 October (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Konstantinos Tyros

Titre/ Some Density Ramsey type results

Abstract/ Özet:

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.

Date/ gün: 12 October (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Özgür Martin

Titre/ Başlık:Disjoint dynamics of linear operators

Abstract/ Özet:

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.

Date/ gün: 20 Avril (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Gönenç Onay

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 13 Avril (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Olcay Coşkun

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 30 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Emine Şule Yazıcı

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 23 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Oğuzhan Kaya

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 16 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Münevver Çelik

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 09 Mars (Mercredi)

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Hironori Shiga

Titre/ Başlık: Number theory through the hypergeometric function

Abstract/ Özet: To be announced

Date/ gün: 23 Décembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Yusuf Danışman

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 16 Décembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Stamatis Pouliasis

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 02 Décembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Çagrı Karakurt

Titre/ Başlık:To be announced

Abstract/ Özet: To be announced

Date/ gün: 18 Novembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Hugues Randriambololona

Titre/ Başlık: To be announced

Abstract/ Özet: To be announced

Date/ gün: 11 Novembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Zafeirakis Zafeirakopoulos

Titre/ Başlık:Polyhedral Omega: A new linear Diophantine system solver

Abstract/ Özet: 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.

Date/ gün: 4 Novembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Manfred Hartl

Titre/ Başlık: To be announced

Abstract/ Özet: To be announced

Date/ gün: 4 Novembre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Jose Luis Cisneros

Titre/ Başlık: On the topology of real analytic maps

Abstract/ Özet: 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.

Date/ gün: 21 Octobre

Lieu /yer: Galatasaray Üniversitesi FEF 9.

Conférencier/ konuşmacı: Katsampekis Anargyros

Titre/ Başlık: Minimal generators of toric ideals associated to numerical semigroups spanned by four positive integers

Abstract Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: İlker İnam

Titre/ başlık: Some Problems and A Possible Conjecture On Half-Integral Weight Modular Forms

Résumé/Özet: 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).

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Seher Tutdere

Titre/ başlık: On the Torsion-Limit for Algebraic Function Fields

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Mark Spivakovsky

Titre/ başlık: On the Torsion-Limit for Algebraic Function Fields

Résumé/Özet: Click here.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Ekin Özman

Titre/ başlık: The p ranks of Prym varieties

Résumé/Özet: 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

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Arzu Boysal

Titre/ başlık: Rational conformal filed theory for pointed stable curves

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Aydın Aytuna

Titre/ başlık: Parabolic Stein Manifolds

Résumé/Özet: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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Jiro Sekiguchi

Titre/ başlık: A generalization of Okubo type differential equations and flat structures

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Emre Mengi

Titre/ başlık: Nonlinear Eigenvalue Problems with Specified Eigenvalues

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Susumu Tanabé

Titre/ başlık: Geometry of oscillating integrals and Dubrovin conjecture

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Haydar GÖRAL

Titre/ başlık: Algebraic Numbers with Small Height Elements

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Hadia Messaoudene

Titre/ başlık: Comparaison des classes d'opérateurs; de Joël Anderson et la classe des opérateurs finis

Résumé/Özet: 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).

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Türker Bıyıkoğlu

Titre/ başlık: Entropy, Assortativity, and Hierarchical Structures in Networks

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: İrfan ŞİAP

Titre/ başlık: Algebraic Codes and Some Recent Studies

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Emre Alkan

Titre/ başlık: Special values of L-functions and Diophantine approximation type results on the real line

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Piotr Kowalski

Titre/ başlık: Recovering a field from a one-dimensional structure

Résumé/Özet: 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).

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Michel Lavrauw

Titre/ başlık: Field reduction in finite geometry

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi, FEF 09.

Conférencier/ konuşmacı: Olivier Le Gal

Titre/ başlık: O-minimalité et champs de vecteurs

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Deniz Karlı

Titre/ başlık: Stable processes and bounded L^p operators

Résumé/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Serap Gürer

Titre/ başlık: Topologie algébrique des espaces difféologiques

Résumé / Özet : 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Handan Yıldırım

Titre/ başlık: On Legendrian dualities for the pseudo-spheres in Lorentz - Minkowski space

Abstract/Özet: Click here) for the abstract.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Ian Morrison

Titre/ başlık: GIT of Hilbert schemes of curves linearized in fixed degree and applications

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Cem Güneri

Titre/ başlık: Algebraic Curves over Finite Fields and Their Rational Points

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Tekin Dereli

Titre/ başlık: Quarks: Who will prove the color confinement conjecture? Mathematicians or Physicists?

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Abdenacer Makhlouf

Titre/ başlık: From Generalized integration to Twisted Rota-Baxter algebras

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Patrick Popescu Pampu

Titre/ başlık: The kite of a plane curve singularity

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Ferit Öztürk

Titre/ başlık: Real 3-manifolds can be obtained from real 3-sphere via surgery

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Sevgi Perek

Titre/ başlık: İş Yaşamında Yönetici ve Yaşam Koçluğu

Abstract/Özet: Konuşma Özeti.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Serkan Sütlü

Titre/ başlık: Characteristic classes of foliations via SAYD-twisted cocycles

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Aybike Özer

Titre/ başlık: Dualities in string theory

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Hatice Boylan

Titre/ başlık: Finite dimensional representations of SL_2 over maximal order in a number field

Abstract/Özet: 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."

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Ayhan Gunaydin

Titre/ başlık: Uniform Versions of the Mordell-Lang Conjecture for Multiplicative Groups

Abstract/Özet: 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.

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Kazim Büyükboduk

Titre/ başlık: An asymptotic Birch and Swinnerton-Dyer Conjecture

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Nilay Duruk Mutlubaş

Titre/ başlık: On periodic solutions of a model equation for surface waves of moderate amplitude in shallow water

Abstract/Özet: 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.

Lieu /yer: IMBM (note the unusual place).

Conférencier/ konuşmacı: Mutsuo Oka

Titre/ başlık: Mixed functions of strongly polar weighted homogeneous face type

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: William Gillam

Titre/ başlık: Logarithmic structures in algebraic and differential geometry

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Serge Randriambololona

Titre/ başlık: Un survol de l'o-minimalité et de quelques unes de ses applications

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Asli Deniz

Titre/ başlık: Introduction to Holomorphic Dynamics: An Extension of Holomorphic Motion

Abstract/Özet: 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.

Lieu /yer: Galatasaray Üniversitesi FEF 09.

Conférencier/ konuşmacı: Şükrü Yalçınkaya

Titre/ başlık: Black Box Groups

Abstract/Özet: 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.

- Date/ gün: 29 mai (mercredi) 15:00

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Ayşe Berkman

Titre/ başlık: Characterizing Groups of Finite Morley Rank via Their Actions

Abstract/Özet: 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.

- Date/ gün: 22 Mayıs (çarşamba) 15:00

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Speaker /konuşmacı: Evrim Hilal Erdamar (Sermaye Piyasası Kurulu)

Title/ başlık: Comovement between stock and bond return in Turkey.

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.

- Date/ gün: 15 mai (mercredi) 15:00

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Athanase Papadopoulos

Titre/ başlık: Structure métrique de l'espace de Teichmüller

- Date/ gün: 8 mai (mercredi) 15:00

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Gönenç Onay

Titre/ başlık: Valued Difference Fields

Resumé/özet: 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.

- Date/gün: April 22 and 29, 2013 14.00

Lieu/ yer: Galatasaray University, FEF 9

Conférencier/Konuşmacı: Evelia Garcia Barroso (Universidad de La Laguna-Tenerife)

Title: Resolution of singularities of plane curves I-II

- Date/gün: April 24, 2013 15.00

Lieu/ yer: Galatasaray University, FEF 10

Conférencier/Konuşmacı: Evelia Garcia Barroso (Universidad de La Laguna-Tenerife)

Title: A criterion of irreducibility for complex series in two variables.

Abstract: 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.

Working Group

Date: April 25-26-30, 2013 14:00 Place: Galatasaray University, FEF 10 Title: Invariants of plane curve singularities Dates: April 25-26-30 Time: 14:00

- Date/gün: 3 avril (mercredi) 15:00

Lieu /yer: Galatasaray Üniversitesi FEF 10.

Conférencier/ konuşmacı: Burak Özbağcı

Titre/ başlık: Exotic Stein fillings with arbitrary fundamental group

Résumé: 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)

- Date/Gün: 22 Mars 2013 10:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Masaaki Yoshida (Université Kyushu)

Abstract/Özet : 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.

- Date/Gün: 20 Mars 2013 10.30 et 15.00

Lieu/Yer: Galatasaray Üniversitesi FEF 8 - FEF 10

Conférencier/Konuşmacı: Masaaki Yoshida

Titre/Başlık: Schwarz maps for hypergeometric functions

Abstract/Özet: 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

- Date/Gün: 13 Mars 2013 13:30

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Jean-Paul Brasselet (CIRM, Marseille)

Titre/Başlık: Orbits divisors on toric varieties.

- Date/Gün: 11 Mars 2013 14:00

Lieu/Yer: Galatasaray Üniversitesi FEF 9

Conférencier/Konuşmacı: Jean-Paul Brasselet (CIRM, Marseille)

Titre/Başlık: Projective Toric Varieties.

- Date/Gün: 27 Février (çarşamba) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Refik Arkut

Titre/Başlık: Internet, Karmaşıklık, MOOC ve Gelecekte Eğitim.

Abstract/Özet: 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.

- Date/Gün: 10 Janvier (jeudi) 11:00

Lieu/Yer: Galatasaray Üniversitesi FEF 8

Conférencier/Konuşmacı: Thomas Hudson

Titre/Başlık: An extension of Schubert polynomials for connected K-theory using algebraic cobordism.

Abstract/Özet: 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.

- Date/Gün: 26 decembre (mercredi) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Alp Bassa

Titre/Başlık: Elliptic Curves, Drinfeld Modules and Curves over Finite Fields

Abstract: 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.

- Date/Gün: 19 Aralık (çarşamba) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Kamel Haouam

Titre/Başlık: Qu'est-ce que la didactique des Mathématiques?

Abstract: 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.

- Date/Gün: 12 Aralık (çarşamba) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: İrem Portakal

Titre/Başlık: Quivers, polytopes and toric varieties

Abstract: 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.

- Date/Gün: 30 Novembre(vendredi) 13:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Frédéric Chapoton

Titre/Başlık: Combinatoire des triangulations

Abstract: 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.

- Date/Gün: 28 Kasım (çarşamba) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Frédéric Chapoton

Titre/Başlık: Tree-indexed series

Abstract: 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.

- Date/Gün: 14 novembre (mercredi) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Müge Taşkın

Titre/Başlık: Tower tableaux

Abstract: 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.

- Date/Tarih: 5 Kasım (pazartesi) 15:00

Place/Yer: Galatasaray Üniversitesi FEF 10.

Speaker/Konuşmacı: Vasile Berinde

Title/Başlık: Some numerical aspects of fixed point iterative methods for solving nonlinear optimization problems

- Date/Gün: 31 octobre (mercredi) 15:00

Lieu/Yer: Galatasaray Üniversitesi FEF 10

Conférencier/Konuşmacı: Stepan Orevkov

Titre/ başlık: Real algebraic and real pseudoholomorphic curves

Abstract: 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.

- Gün: 25 Mayıs (Cuma) 14:30

Yer: Galatasaray Üniversitesi FEF9

Speaker/konuşmacı: Emel Bilgin (Univ. Essen)

Title/başlık: Classes of hypersurfaces of low degree in the Grothendick ring of varieties K_0(Var_k).

- Gün: 15 Mayıs (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF 10

Speaker/konuşmacı: Murat Turhan (Yıldız Teknik Üniversitesi)

Title/başlık: Hirota type discretization

Abstract/özet : 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.

- Gün: 10 Mayıs (Perşembe) 16:00

Yer: Galatasaray Üniversitesi FEF 8

Speaker/konuşmacı: Nicolas Vayatis (ENS, Cachan)

Title/Başlık: Statistical Learning Theory: a playground for the mathematics of prediction.

Abstract/Özet: 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.

- Gün: 24 Nisan (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/konuşmacı: Mihai Tibar (Univ. Lille 1, France)

Title/Başlık: Betti numbers of polynomials

Abstract/Özet: 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.

- Gün: 17 Nisan (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/konuşmacı: Haluk Şengün (University of Warwick)

Title/Başlık: Cohomology of Bianchi Groups

Abstract/Özet: 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.

- Gün: 10 Nisan (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/konuşmacı: Vincent Labatut (Université de Galatasaray)

Title/Başlık: Complex Networks Analysis

Abstract/Özet: 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.

- Gün: 3 Nisan (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/konuşmacı: Mark Spivakovsky (Université de Toulouse)

Başlık/Title: Introduction to the problem of resolution of singularities

Özet/Abstract: 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".

- Gün: 20 Mart (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/Konuşmacı: Jiro Sekiguchi (Tokyo University of Agriculture and Technology)

Başlık/Title: Free Divisors and Painlevé Equations after M. Kato

Özet/Abstract: 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.

- Gün: 13 Mart (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF10

Speaker/Konuşmacı: Richard Gonzales (Galatasaray University)

Başlık/Title: Standard group embeddings and divided differences operators.

Özet/Abstract: 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.

- Gün: 28 Şubat (Salı) 16:00

Yer: Galatasaray Üniversitesi FEF 10

Konuşmacı/Speaker: Dr. Ayşe Altıntaş (Yıldız Teknik Üniversitesi)

Başlık /Title: Examples of finitely determined map-germs.

Özet/Abstract -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.

- Gün: 29 Aralık 2011 (Perşembe) 16:00

Yer: Galatasaray Üniversitesi FEF9

Konuşmacı/Speaker : Bernard Teissier (Institut Mathématique de Jussieu, Equipe Géométrie et Dynamique)

Başlık /Title : On the Lojasiewicz exponent.

Özet/Abstract: 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.

- Gün: 8 Aralık 2011 (Perşembe) 16:00

Yer: Galatasaray Üniversitesi FEF9

Konuşmacı/Speaker - Arnaldo Garcia (IMPA at Rio de Janeiro, Sabancı Üniversitesi)

Başlık /Title - Asymptotics on codes and on curves over finite fields.

Özet/Abstract- 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.

- Gün: 22 Aralık 2011 (Perşembe) 16:00

Yer: Galatasaray Üniversitesi FEF9

Speaker/Konuşmacı: Cemsinan Deliduman (Mimar Sinan Güzel Sanat Üniversitesi)

Title/Başlık : Entanglement Swapping Model of DNA Replication

Abstract/Özet: 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.

- Gün: 3 Kasım 2011 (Perşembe) 16:00

Yer: Galatasaray Üniversitesi FEF9

Konuşmacı/Speaker: Ayberk Zeytin (Galatasaray University)

Başlık/Title : Polygonal decompositions of the sphere and ball quotients

Özet/Abstract: 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.)

- Lundi 9 mai 2011, 15h30-16h30, salle P20.

Johannes HUEBSCHMANN, Université des sciences et technologies de Lille.

Singular Poisson-Kähler geometry of stratified Kähler spaces.

Abstract

- Mercredi 4 et jeudi 5 mai 2011, 16h00-18h00, salle FEF 8 (mercredi) et FEF 1
(jeudi).

Eugene HA, Galatasaray Üniversitesi.

Galois Theory from Galois' Perspective.

Abstract. 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.

- Lundi 25 avril 2011, 15h00-16h00, salle P20.

Müge KANUNI, Boğaziçi Üniversitesi.

Discrete Structures in Algebra.

Abstract. 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.

- Lundi 4 avril 2011, 15h00-16h00, salle P20.

Meral TOSUN, Université Galatasaray.

Good slices for simple elliptic singularities.

Abstract. 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.

- Jeudi 24 mars 2011, 9h00-11h00, salle FEF 5.

Athanase PAPADOPOULOS, Institut de Recherche Mathématique Avancée, Strasbourg.

Espaces métriques généralisés 2.

- Mercredi 23 mars 2011, 16h00-18h00, salle FEF 10.

Athanase PAPADOPOULOS, Institut de Recherche Mathématique Avancée, Strasbourg.

Espaces métriques généralisés 1.

- Lundi 21 mars 2011, 16h00-17h00, salle FEF 7.

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.

Abstract. 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.

- Lundi 21 mars 2011, 15h00-16h00, salle FEF 7.

Athanase PAPADOPOULOS, Institut de Recherche Mathématique Avancée, Strasbourg.

La géométrie de Finsler.

- Mercredi 16 mars 2011, 15h00-16h00, salle FEF 9.

Eric SOCCORSI, centre de physique théorique, Marseille.

Résolution des équations différentielles par la méthode des élements finis.

Abstract. J'expliquerai comment on résout "numériquement" une EDP en prenant pour simplifier un exemple d'EDO.

- Lundi 14 mars 2011, 16h00-17h00, salle FEF 7.

Eric SOCCORSI, centre de physique théorique, Marseille.

Lipschitz stability in an inverse problem for non autonomous magnetic Schrödinger equations.

Abstract. 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.

- Lundi 14 mars 2011, 15h00-16h00, salle FEF 7.

Oleg BELEGRADEK, İstanbul Bilgi Üniversitesi.

How similar can non-isomorphic algebraic structures be?

Abstract. 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.

- Mercredi 9 mars 2011, 15h00-16h00, salle FEF 10.

Jawad SNOUSSI, Universidad Nacional Autónoma de México.

Modifiactions des singularités.

Abstract. Nous expliquerons les concepts d'éclatement, de normalisation, de modification de Nash et leur relations avec la résolution des singularités

- Lundi 7 mars 2011, 15h00-16h00, salle FEF 4.

Jawad SNOUSSI, Universidad Nacional Autónoma de México.

Equisingularity in complex surfaces.

Abstract. 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.

- Lundi 28 février 2011, 15h00-16h00, salle P 23.

Eugene HA, Université Galatasaray & Fields Institute, Toronto.

The problem of cohomology for an Arakelov divisor.

Abstract. 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).

- Vendredi 7 janvier 2011, 15h00-16h00, salle FEF 1.

Gülay KAYA, Université Galatasaray.

The Groebner fan of a polynomial ideal.

- Lundi 20 décembre 2010, 15h00-16h00, salle FEF 9.

Muhammed ULUDAĞ, Université Galatasaray.

Hypergeometric Galois Actions.

- Lundi 6 décembre 2010, 15h00-16h00, salle FEF 9.

Cédric MILLIET, Université Galatasaray.

Quelques mots de théorie des modèles.

Abstract. 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.

- Mercredi 24 novembre 2010, 17h15-18h15, salle FEF 9.

Susumu TANABE, Université Galatasaray.

Invariants of hypergeometric groups for Calabi--Yau complete intersections in weighted projective spaces

Abstract. 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.

- Vendredi 5 novembre 2010, 10h-12h, salle P 19.

Xavier BRESSAUD, Institut de Mathématiques de Toulouse.

Introduction à la dynamique symbolique. (2/2)

- Jeudi 4 novembre 2010, 10h-11h, salle FEF 9.

Xavier BRESSAUD, Institut de Mathématiques de Toulouse.

Introduction à la dynamique symbolique. (1/2)

- Mercredi 27 octobre 2010, 16h00, salle FEF 10.

Hervé GAUSSIER, Institut Joseph Fourier, Grenoble

Pseudoholomorphic curves and applications

Abstract. 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.

- Mardi 26 octobre 2010, 15h00, salle FEF 1.

Hervé GAUSSIER, Institut Joseph Fourier, Grenoble

Géométrie et calcul infinitésimal. Séminaire introductif à destination des étudiants

Abstract. 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.

© GSÜ Math. Tüm hakları saklıdır.