Galatasaray Üniversitesi Matematik Bölümü

Galatasaray Üniversitesi · Matematik Bölümü

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Research Seminars

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

2023-2024 (Organized by Adam Ouzeri and Gönenç Onay)

Date/gün: May 8th, 16:00
Lieu/yer: Galatasaray Üniversitesi, room I222.
Konuşmacı/Invité/Guest: Zeynel Ulusan, Computer Engineering Department - Koç University

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.

Date/gün: April 17th, 15:00
Lieu/yer: Galatasaray Üniversitesi, room I204.
Konuşmacı/Invité/Guest: Sibel Özkan, Department of Mathematics - Gebze Technical University

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.

Date/gün: March 22, 15:00
Lieu/yer: Galatasaray Üniversitesi, room I109.
Konuşmacı/Invité/Guest: Athanase Papadopoulos, ITI CREAA - IRMA - University of Strasbourg

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.

Date/gün: February 28, 15:00
Lieu/yer: Galatasaray Üniversitesi, room I204.
Konuşmacı/Invité/Guest: Ceren Gürkan, Faculty of Engineering and Natural Sciences - Kadir Has University

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.

Date/ gün: 21 February 15:00
Lieu /yer: Galatasaray Üniversitesi, room I204.
Konuşmacı/Invité/Guest: Çağrı Diner, Boğaziçi University

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.

Date/ gün: 14 February 15:00
Lieu /yer: Galatasaray Üniversitesi, room I204.
Konuşmacı/Invité/Guest: Zeynep Hassanzadeh, Istanbul Technical University

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.

Date/ gün: 27 December 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Çağtay Yıldız, University of Tübingen

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.

Date/ gün: 20 December 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Sylvain Lavau, Aristotle University of Thessaloniki

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.

Date/ gün: 13 December 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Mounir Nisse, Xiamen University Malaysia

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.

Date/ gün: 6 December 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Salah Mehdi, Institute Elie Cartan of Lorraine - University of Lorraine

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.

Date/ gün: 22 November 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Türkü Özlüm Çelik, College of Sciences - Koç University

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.

Date/ gün: 15 November 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Mark Spivakovsky, Galatasaray University

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 $d$.

Date/ gün: 8 November 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Adam Ouzeri, Galatasaray University

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.

Date/gün: October 18, 15:00
Lieu/yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: José Luis Cisneros-Molina, Institute of Mathematics - National Autonomous University of Mexico.

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 mixed GSV-index and it generalizes the classical GSV-index defined by Gomez-Mont, Seade and Verjovsky, i.e., if the function $f$ is holomorphic, then the mixed GSV-index coincides with the GSV-index. Furthermore, the mixed GSV-index is a lifting to $\mathbb{Z}$ of the $\mathbb{Z}_2$-valued real GSV-index defined by Aguilar, Seade and Verjovsky. As applications we prove that the mixed GSV-index is equal to the Poincar\'e-Hopf index of $v$ on a Milnor fiber. If $f$ also satisfies the strong Milnor condition, i.~e., for every $\epsilon>0$ (small enough) the map $\frac{f}{\|f\|}\colon \mathbb{S}_\epsilon \setminus L_f \to \mathbb{S}^1$ is a fiber bundle, we prove that the mixed GSV-index is equal to the curvatura integra of $f$ defined by Cisneros-Molina, Grulha and Seade based on the curvatura integra defined by Kervaire.

2022-2023 (Organized by Ahmad Rafiqi)

Date/ gün: October 12, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Tülay Ayyıldız Aksoy, Karadeniz Technical University and Istanbul Technical University.

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.

Date/ gün: October 26, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Ferhat Kürüz, Istanbul Gelişim University.

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.

Date/ gün: November 02, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Soner Aydınlık, Doğuş University.

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.

Date/ gün: November 09, 15:00 (First talk)
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest:Daniel Massart, Institut Montpelliérain Alexander Grothendieck, Université de Montpellier.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Date/ gün: November 09, 16:00 (Second talk)
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: TBA.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Date/ gün: November 16, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Figen Öztoprak Topkaya, Istanbul Technical University.

Başlık/Titre/Title: TBAŞafak Özden

Özet/Résumé/ Abstract: TBA

Date/ gün: November 23, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Jose Seade, National University of Mexico (UNAM).

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Date/ gün: November 30, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Mesut Ürün.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Date/ gün: December 07, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Şafak Özden, Tulane University.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

Date/ gün: December 14, 15:00
Lieu /yer: Galatasaray Üniversitesi, room H304.
Konuşmacı/Invité/Guest: Elif Üsküplü, University of Southern California.

Başlık/Titre/Title: TBA

Özet/Résumé/ Abstract: TBA

2021-2022 (Organized by Özge Ülkem)

Date/ gün: 8 December 15:00
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.

Date/ gün: 22 December 15:00
Lieu /yer: Galatasaray Üniversitesi, room A324.
Konuşmacı/Invité/Guest: Gönenç Onay

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

Date/ gün: 29 December 15:00
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

Date/ gün: 12 January 15:00
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.

Date/ gün: 26 January 15:00
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.

Date/ gün: 23 February 15:00
Lieu /yer: Galatasaray Üniversitesi, room H306
Konuşmacı/Invité/Guest: Fatma Çiçek

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

Date/ gün: 9 March 15:00
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)

Date/ gün: 23 March 15:00
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).

Date/ gün: 6 April 15:00
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.

Date/ gün: 20 April 15:00
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.

Date/ gün: 11 May 15:00
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.

Date/ gün: 25 May 15:00
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)

Unless specified the talks will take place in room 10 FEF at 14:00

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.

2016-2017 (Organized by Oğuzhan Kaya)

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.

2015-2016 (Organized by Serap Gürer)

Date/ gün: 20 Avril (Mercredi)
Lieu /yer: Galatasaray Üniversitesi FEF 9.
Conférencier/ konuşmacı: Gönenç Onay

Titre/ Başlık:To be announced