BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oğuz Şavk (Boğaziçi Üniversitesi) DTSTART:20211105T140000Z DTEND:20211105T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/1 DESCRIPTION:Title: Classical and new plumbings bounding contractible manifolds and homolog y balls\nby Oğuz Şavk (Boğaziçi Üniversitesi) as part of Mimar Si nan University Mathematics Seminars\n\n\nAbstract\nA central problem in lo w-dimensional topology asks which \nhomology 3-spheres bound contractible 4-manifolds and homology 4-balls. \nIn this talk\, we address this problem for plumbed 3-manifolds and we \npresent the classical and new results to gether. Our approach is based on \nMazur’s famous argument and its gener alization which provides a \nunification of all results.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Can Ozan Oğuz (Galatasaray Üniversitesi) DTSTART:20211112T140000Z DTEND:20211112T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/2 DESCRIPTION:Title: Tekrarlı Çelenk Çarpımlarında Kısıtlama ve Yükseltme\nby Can Ozan Oğuz (Galatasaray Üniversitesi) as part of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nSimetrik grubun temsilleri pek çok se bepten dolayı ilgi görüyor. 2010 yılında Khovanov\, bu temsiller üze rindeki kısıtlama ve yükseltme operatörlerinin ilişkilerinden oluşan bir kategori tanımladı: Heisenberg kategorisi. Devamında bu çalışma simetrik grubun Frobenius cebirleri ile çelenk çarpımlarına genelleş tirildi. Biz konuyu farklı bir yönde\, simetrik grupların birbirleri il e tekrarlı çelenk çarpımları için ele alıyoruz. Bu durumda kısıtl ama ve yükseltme operatörleri arasındaki ilişkileri tarif eden bir kat egorinin yapısını kısmi olarak ortaya koyuyoruz. Mee Seong Im ile orta k çalışmamızdır.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Berrin Şentürk (TED Üniversitesi) DTSTART:20211126T140000Z DTEND:20211126T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/3 DESCRIPTION:Title: Free group actions on products of spheres\nby Berrin Şentürk (TED Üniversitesi) as part of Mimar Sinan University Mathematics Seminars\n\n\ nAbstract\nOne of the engaging problems in the field of algebraic topology is the \nclassification of group actions on manifolds. In this talk\, we consider \nfree finite group actions on a product of spheres. We will disc uss the \nupper bound for the rank of the group that can act freely on thi s \nproduct by using algebraic methods.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Cihan Okay (Bilkent Üniversitesi) DTSTART:20220107T140000Z DTEND:20220107T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/4 DESCRIPTION:Title: Homotopy classification of operator solutions of linear systems\nby Cihan Okay (Bilkent Üniversitesi) as part of Mimar Sinan University Mathe matics Seminars\n\n\nAbstract\nLinear systems of equations over a finite f ield play an important role in quantum information theory. Instead of look ing for solutions over the base field one can look for solutions (in a cer tain sense) over the unitary group\, which are called operator solutions. The data of this system of equations can be expressed using a hypergraph a nd the operator solutions can be studied from a topological point of view by considering certain topological realizations of these hypergraphs. In t his talk I will describe how homotopical methods provide a way to classify operator solutions of linear systems. Our basic approach is to interpret operator solutions as maps from a topological realization of the hypergrap h to a certain classifying space first introduced by Adem-Cohen-Torres Gie se.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Şeyda İpek (Carleton University) DTSTART:20211119T140000Z DTEND:20211119T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/5 DESCRIPTION:Title: Fundamental symmetries of nature\nby Şeyda İpek (Carleton Universi ty) as part of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\n The building blocks of our universe\, elementary particles\, obey some sim ple rules based on certain symmetry arguments. The most basic interactions of elementary particles can be described by the Standard Model\, whose un derlying symmetry structure is described by the group structure SU(3)xSU(2 )xU(1). There are more symmetries--sometimes empirical\, sometimes acciden tal--we encounter when studying elementary particles. Some of these symmet ries must be broken in order for our universe to work\, e.g. based on our observations matter--antimatter symmetry is not a good symmetry since we d o not have any antimatter in the universe while the SM has this symmetry. I will give a broad overview of the interconnection between particle phys ics and symmetries and how they help us build theoretical models of our un iverse.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Özgür Martin (MSGSÜ) DTSTART:20211203T140000Z DTEND:20211203T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/6 DESCRIPTION:Title: Bolstering Stochastic Gradient Descent with Model Building\nby Özg ür Martin (MSGSÜ) as part of Mimar Sinan University Mathematics Seminars \n\n\nAbstract\nStochastic gradient descent method and its variants consti tute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Althoug h this tuning process can require large computational costs\, recent work has shown that these costs can be reduced by line search methods that iter atively adjust the stepsize. In this talk\, we will introduce an alternati ve approach to stochastic line search by using a new algorithm based on fo rward step model building. This model building step incorporates a second- order information that allows adjusting not only the stepsize but also the search direction.\n\nThis is a joint work with S. I. Birbil\, G. Onay\, a nd F. Öztoprak.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Esma Dirican Erdal (Yeditepe Üniversitesi) DTSTART:20220114T140000Z DTEND:20220114T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/7 DESCRIPTION:Title: Multiplicative Gluing Formulas for the R-torsion of (n-2)-Connected Clos ed pi-Manifolds\nby Esma Dirican Erdal (Yeditepe Üniversitesi) as par t of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nLet $M$ be a closed orientable $(n-2)$-connected $2n$-dimensional $\\pi$-manifold. S uch a manifold $M$ can be decomposed as a connected sum of certain simpler manifolds. In this talk\, by using such connected sum decompositions\, we will give multiplicative gluing formulas that express the Reidemeister to rsion of $M$ with untwisted $\\mathbb{R}$-coefficients in terms of Reideme ister torsions of its building blocks. This is a joint work with Yaşar S özen.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Asgar Jamneshan (Koç Üniversitesi) DTSTART:20211217T140000Z DTEND:20211217T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/8 DESCRIPTION:Title: The structure of arbitrary Conze-Lesigne systems\nby Asgar Jamneshan (Koç Üniversitesi) as part of Mimar Sinan University Mathematics Semina rs\n\n\nAbstract\nWe consider probability-preserving dynamical systems fro m countable abelian group actions. Such a system is said to be a Conze-Le signe system if it is equal to its second Host-Kra-Ziegler factor (these f actors arise in the study of multiple recurrence and play a foundational r ole in related areas in additive combinatorics and number theory). We pro vide a classification of Conze-Lesigne systems in terms of algebraic data. More precisely\, we show that an arbitrary Conze-Lesigne system is an in verse limit of translational systems arising from locally compact nilpoten t groups of nilpotency class 2 quotient by a lattice. Results of this typ e were previously known when the acting group is finitely generated or a d irect sum of cyclic groups. The talk aims at introducing the field. If t ime permits\, we will present an application to additive combinatorics. T he talk is based on recent joint works with Or Shalom and Terence Tao.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Shigeo Koshitani (Chiba University) DTSTART:20220121T140000Z DTEND:20220121T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/9 DESCRIPTION:Title: What has happened\, is happening and is going to happen in representatio n theory of finite groups\nby Shigeo Koshitani (Chiba University) as p art of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nWe are g oing to talk on representation theory of finite groups\,\nespecially on mo dular representation theory due to Richard Brauer\n(1901--1977) in the las t several decades. More precisely by starting off\nkind of history of repr esentation theory and then hopefully we would like to\nreach to recent big results on some of the local-global conjectures\noriginally due to Brauer . This is sort of general talk\, so almost no\nadvanced knowledge should b e needed except the definitions of groups\,\nrings\, fields\, and matrices .\n LOCATION:https://researchseminars.org/talk/MSGSUMath/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Aslıhan Ünsal (Sabancı Üniversitesi) DTSTART:20211210T140000Z DTEND:20211210T150000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/10 DESCRIPTION:Title: Innovative Approaches in STEM* Education\nby Aslıhan Ünsal (Saban cı Üniversitesi) as part of Mimar Sinan University Mathematics Seminars\ n\n\nAbstract\nIn a rapidly changing world\, we need to consider the follo wing two points while planning higher education\; change in student profil es and their learning needs\; demand for collaborative efforts of experts to tackle world-wide problems\, such as global warming. In 2013\, at Saban ci University\, we started to redesign our freshman science course to bett er prepare our students for their careers after graduation according to g lobal needs. In this talk\, I will be sharing the design and the implement ation process of our integrated science course. \n\n*: Science\, Technolog y\, Engineering\, Mathematics.\n\nKeywords: Active learning\; Peer support \; Backward course design\n LOCATION:https://researchseminars.org/talk/MSGSUMath/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Serdar Ay (Atılım Üniversitesi) DTSTART:20211224T130000Z DTEND:20211224T140000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/11 DESCRIPTION:Title: Adjointable Operators of Barreled VH-Spaces is a Locally $C^*$-Algebra \nby Serdar Ay (Atılım Üniversitesi) as part of Mimar Sinan Univers ity Mathematics Seminars\n\n\nAbstract\nA VH-space (Vector Hilbert Space i n the sense of Loynes) is a complex complete locally convex space with a s uitable ordered vector space valued inner product. Examples of VH-spaces i nclude\, but is not limited to\, the chain of locally Hilbert $C^*$-module s\, Hilbert $C^*$-modules and Hilbert Spaces\n We prove that\, on a Bar reled VH-Space\, the set of all adjointable operators consists of bounded operators and is a Locally $C^*$-Algebra\, generalizing the well known cor responding fact from the theory of Locally Hilbert $C^*$-modules. \n\n We pick a consequence of this result in the dilation theory of VH-Spaces a nd show that\, under the barreledness assumption\, a necessary and suffici ent condition for the existence of VH-space linearisations\, equivalently\ , of reproducing kernel VH-Spaces\, is satisfied automatically.\n\nThe tal k is not at our usual time\, it will be at 16.00\n LOCATION:https://researchseminars.org/talk/MSGSUMath/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantin-Cosmin Todea (Technical University of Cluj-Napoca) DTSTART:20220330T120000Z DTEND:20220330T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/12 DESCRIPTION:Title: Nontriviality of the first Hochschild cohomology of some block algebras of finite groups\nby Constantin-Cosmin Todea (Technical University o f Cluj-Napoca) as part of Mimar Sinan University Mathematics Seminars\n\n\ nAbstract\nHochschild cohomology $\\mathrm{HH}^*(A)$ of an associative (un ital) $k$-algebra $A$ (here $k$ is a field) has a rich structure. First Ho chschild\ncohomology $\\mathrm{HH}^1(A)$ is isomorphic to the quotient of the space of $k$-linear derivations\nof $A$ modulo its inner derivations. In the context of modular representation theory\, if the field $k$ has cha racteristic $p$ and $G$ is a finite group\, an indecomposable direct algeb ra factor $B$ of the group algebra $kG$ is called block algebra. Is $\\ma thrm{HH}^1(B)$ nontrivial for any block algebra $B$ with nontrivial defec t group? This is a question launched by Markus Linckelmann at the ICRA 201 6. We explain the basic facts needed to understand this question. We give methods to investigate the nontriviality of the first Hochschild cohomol ogy of some twisted group algebras. As a consequence we show that for some block algebras\, with nontrivial defect groups\, the first Hochschild coh omology is nontrivial.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehmet Akif Erdal (Yeditepe University) DTSTART:20220406T120000Z DTEND:20220406T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/13 DESCRIPTION:Title: An Elmendorf-Piacenza style Theorem for actions of monoids\nby Mehm et Akif Erdal (Yeditepe University) as part of Mimar Sinan University Math ematics Seminars\n\n\nAbstract\nIn this talk I will describe a homotopy th eory for actions of monoids that is built by analyzing their ``reversible parts". Let $M$ be a monoid. For each submonoid $N\\leq M$ let $G(N)$ be t he group completion of $N$. Given an $M$-space $X$ and a submonoid $N\\leq M$\, we associate a $G(N)$-space $q_*^N(X)$ which sorts out “symmetries ” of the $N$-space $X$ with the restricted $N$-action. By using these $q _*^N$'s we induce a model structure on the category of $M$-spaces and $M$- equivariant and show that this model structure is Quillen equivalent to th e projective model structure on the category of contravariant $\\mathbf{O} (M)$-diagrams of spaces\, where $\\mathbf{O}(M)$ is the category whose obj ects are induced orbits $M\\times_N G(N)/H$ for each $N\\leq M$ and $H\\le q G(N)$ and morphisms are $M$-equivariant maps. Finally\, if time permits\ , I will state some applications.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nadia Romero (Universidad de Guanajuato) DTSTART:20220427T130000Z DTEND:20220427T140000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/14 DESCRIPTION:Title: Green fields\nby Nadia Romero (Universidad de Guanajuato) as part o f Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nGreen fields were discovered by Serge Bouc in 2019. To be precise\, the terminology was introduced at the very end of his paper Relative B-groups\, published in 2019. A Green field is a commutative Green biset functor with no non-trivi al ideals. In this talk I will present some properties of a Green field an d examples of known Green biset functors which are Green fields. This is a joint work with Serge Bouc.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Şükran Gül Erdem (TED University) DTSTART:20220617T100000Z DTEND:20220617T110000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/15 DESCRIPTION:Title: Beauville p-groups\nby Şükran Gül Erdem (TED University) as part of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nBeauville s urfaces are a class of rigid complex surfaces that have many nice geometri c properties. \n A finite group giving rise to such a surface is called a \\textit {Beauville group}.\n What makes them so good to deal with is the fact that they can be described in purely group theoretical terms.\n A finite group $G$ is a Beauville group if $G$ is a $2$-generator group a nd it has a pair of generating sets $\\{x_1\, y_1\\}$ and $\\{x_2\,y_2\\}$ such that\n $\\Sigma (x_1\,y_1) \\cap \\Sigma(x_2\,y_1)=\\{1\\}$ where for $i=1\, 2$\n \\[\n \\Sigma(x_i\,y_i)\n =\n \\bigcup_{g\\in G} \ \\,\n \\Big( \\langle x_i \\rangle^g \\cup \\langle y_i \\rangle^g \\cup \\langle x_iy_i \\rangle^g \\Big).\n \\]\n \n Catanese showed in 20 00 that the abelian Beauville groups are those of the form $C_n \\times C_ n$ with $(n\,6)=1$. \n After abelian groups\, the most natural class of finite groups to consider are nilpotent groups. \n One can easily show t hat the study of nilpotent Beauville groups can be reduced to that of Beau ville $p$-groups.\n \n In this talk we survey a large collection of re sults on Beauville $p$-groups: from the earliest examples of Beauville $p$ -groups to Beauville $p$-groups in the most known families of $p$-groups w ith a good behavior with respect to powers\, such as regular $p$-groups\, powerful $p$-groups\, $p$-central $p$-groups etc.\n \n We further focu s on infinite families of Beauville $p$-groups arising from the quotients of infinite groups such as the free group\, free product and triangle grou ps.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Taro Sakurai (Chiba University) DTSTART:20220323T120000Z DTEND:20220323T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/16 DESCRIPTION:Title: The isomorphism problem for modular group algebras\nby Taro Sakurai (Chiba University) as part of Mimar Sinan University Mathematics Seminars \n\n\nAbstract\nSuppose that two finite p-groups G and H have isomorphic g roup algebras\nover the field with p elements. Are G and H isomorphic? Thi s is a simple\nproblem which is known for more than half a century\, and i t is known to be\nnotoriously hard. Recently this problem has been drawn a ttention again and\nstriking progress was made. I will present a short his tory of the problem\,\nexplain some primary techniques\, and touch upon my latest work with Leo\nMargolis and Mima Stanojkovski.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Neslihan Girgin (MSGSU) DTSTART:20220525T120000Z DTEND:20220525T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/17 DESCRIPTION:Title: A Number Theoretical Approach to the Polynomials over Finite Fields \nby Neslihan Girgin (MSGSU) as part of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nLet q be a prime power and Fq be the finite field with q elements. The explicit constructions\nof irreducible polynomials o ver Fq is one of the main problems in the arithmetic of\nfinite fields whi ch has many applications in several areas such as coding theory\, cryptogr aphy\,\netc. In general\, some recursive methods are preferred to do these constructions using\nrational transformations. \nIn particular\, we are i nterested in methods that are obtained by using\nquadratic transformations . For doing this\, we will first classify and normalize the rational trans formations of degree 2 using the behaviour of the ramified places in the c orresponding rational function field extensions over the finite field Fq. Then we will investigate the constructions using Galois theory and some ba sic observations in group theory. This approach provides to understand the iterative constructions better and gives various generalisations of them. It also helps to determine the requirements put on the initial polynomial s easier.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Semra Öztürk (METU) DTSTART:20220608T120000Z DTEND:20220608T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/19 DESCRIPTION:Title: On m-th roots of nilpotent matrices\nby Semra Öztürk (METU) as pa rt of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nThis talk is based on the paper with the same title which appeared in Electronic Jo urnal of Linear Algebra\, November 2021 it is dedicated to the memory of d ear Professor Cem Tezer.\n\nA new necessary and sufficient condition for t he existence of an m-th root\nof a nilpotent matrix in terms of the multip licities of Jordan blocks is obtained\nand expressed as a system of linear equations with nonnegative integer entries.\nThus\, computation of the Jo rdan form of the m-th power of a nilpotent matrix\nis reduced to a single matrix multiplication\; conversely\, the existence of an m-th\nroot of a n ilpotent matrix is reduced to the existence of a nonnegative integer\nsolu tion to the corresponding system of linear equations. For a singular matri x\nhaving an m-th root with a pair of nilpotent Jordan blocks of sizes s a nd l\,\na new m-th root is constructed by replacing that pair by another o ne of sizes\ns + i and l − i\, for special s\, l\, i. If time permits we can state some results for\nthe existence of m-th roots of A^k for a matr ix A over an arbitrary field that is\na sum of two commuting matrices wher e k ≥ t and t is the nilpotency of the\nnilpotent part of A.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Haldun Özgür Bayındır (City\, University of London) DTSTART:20220413T120000Z DTEND:20220413T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/20 DESCRIPTION:Title: Adjoining roots to ring spectra and algebraic K-theory\nby Haldun Özgür Bayındır (City\, University of London) as part of Mimar Sinan Un iversity Mathematics Seminars\n\n\nAbstract\nThe category of spectra captu res an important part of the complexity of topological spaces while provid ing generalizations of many important notions in homological algebra. \n\n In this work\, we develop a new method to adjoin roots to ring spectra and show that this process results in interesting splittings in algebraic K-t heory.\n\nIn the first part of my talk\, I will provide motivation for alg ebraic K-theory and highly structured ring spectra. After this\, I will di scuss trace methods\, a program that provides computational tools for alge braic K-theory\, and introduce our results.\n\nThis is a joint work in pro gress with Tasos Moulinos and Christian Ausoni.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Max Hoffmann (University of Warsaw) DTSTART:20220420T120000Z DTEND:20220420T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/21 DESCRIPTION:Title: On finite group action and model theory\nby Daniel Max Hoffmann (Un iversity of Warsaw) as part of Mimar Sinan University Mathematics Seminars \n\n\nAbstract\nI will present results from my joint project with Piotr Ko walski. It is about a model-theoretic description of actions of a fixed fi nite group on quite arbitrary structures. More precisely\, take a big mode l M of some stable theory and a group G. Consider the family of all substr uctures of M equipped with a group action (by automorphisms) of G. The qu estion is whether the sub-family of existentially closed (i.e. rich in "so lutions of equations") substructures with a group action of G can be axiom atized\, so whether we can first order statements which correspond to bein g rich in solutions. We will analyze the situation for finite G and expres s the problem in terms involving only the invariants of the group action.\ n LOCATION:https://researchseminars.org/talk/MSGSUMath/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Rizos Sklinos (Chinese Academy of Sciences) DTSTART:20220511T120000Z DTEND:20220511T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/22 DESCRIPTION:Title: Elementary theories of hyperbolic groups\nby Rizos Sklinos (Chinese Academy of Sciences) as part of Mimar Sinan University Mathematics Semina rs\n\n\nAbstract\nThe discovery of non euclidean geometry in the early nin eteenth century had shaken the beliefs and conjectures of more than two th ousand years and changed the picture we had for mathematics\, physics and even philosophy. Lobachevsky and Bolyai independently around 1830 discover ed hyperbolic geometry. A notable distinguish feature of hyperbolic geomet ry is its negative curvature in a way that the sum of angles of a triangle is less than π. Gromov much later in 1987 introduced hyperbolic groups w hich are groups acting “nicely” on hyperbolic spaces\, or equivalently finitely generated groups whose Cayley graphs are “negatively curved” . Main examples are free groups and almost all surface groups. The fascina ting subject of hyperbolic groups touches on many mathematical disciplines such as geometric group theory\, low dimensional topology and combinatori al group theory. It is connected to model theory through a question of Tar ski.\n\nTarski asked around 1946 whether non abelian free groups have the same first order theory. This question proved extremely hard to answer and only after more than fifty years in 2001 Sela and Kharlampovich-Myasnikov answered it positively. Both works are voluminous and have not been fully absorbed yet. The great novelty of the methods and the depth of the neede d results have made it hard to streamline any of the proofs. Despite the d ifficulties there is some considerable progress in the understanding of th e first-order theory of “the free group” and consequently first-order theories of hyperbolic groups from the scopes of basic model theory\, Shel ah’s classification theory and geometric stability. In this talk I will survey what is known about these theories and what are the main open quest ions.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Aslı Güçlükan İlhan (Dokuz Eylül University) DTSTART:20220518T120000Z DTEND:20220518T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/23 DESCRIPTION:Title: Weakly equivariant classification of small covers over a product of sim plices\nby Aslı Güçlükan İlhan (Dokuz Eylül University) as part of Mimar Sinan University Mathematics Seminars\n\n\nAbstract\nA small cove r over an n-dimensional simple convex polytope P is a smooth closed manifo ld with a locally standard $\\mathbb{Z}_2^n$-action whose orbit space can be identified with P. Small covers over P can be classified using characte ristic functions from the set of facets of P to $\\mathbb{Z}_2^n$. In this talk\, we give a weakly $\\mathbb{Z}_2^n$-equivariant classification of s mall covers over a product of simplices in terms of associated digraphs. T his is a joint work with S. Kaan Gürbüzer.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Özge Ülkem (Galatasaray University) DTSTART:20220601T120000Z DTEND:20220601T130000Z DTSTAMP:20260422T090347Z UID:MSGSUMath/24 DESCRIPTION:Title: The moduli space of generalized D-elliptic sheaves\nby Özge Ülkem (Galatasaray University) as part of Mimar Sinan University Mathematics Se minars\n\n\nAbstract\nOne of the fundamental objects of the algebraic numb er theory are elliptic curves. Drinfeld defined analogues of elliptic curv es in the function field setting\, which are now called Drinfeld modules. to prove Langlands correspondence he defined a categorically equivalent no tion\, called elliptic sheaves\, and studied their moduli space. Since the n many generalizations of Drinfeld modules and elliptic sheaves have been worked out. In the first part of this talk we will form the function field and classical setting and discuss similarities between them. Then\, we de fine Drinfeld modules\, discuss the analogy between elliptic curves and Dr infeld modules. In the second part we talk we will define a new generaliza tion of elliptic sheaves\, called “generalized D-elliptic sheaves” and talk on their moduli space and of the uniformization of the latter if tim e permits.\n LOCATION:https://researchseminars.org/talk/MSGSUMath/24/ END:VEVENT END:VCALENDAR