BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pieter Spaas (UCLA) DTSTART:20211102T143000Z DTEND:20211102T154000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/1 DESCRIPTION:Title: Group actions and equivalence relations\nby Pieter Sp aas (UCLA) as part of Koç University Mathematics Seminar\n\n\nAbstract\nG roup actions of a countable group on a measure space give rise to interest ing dynamical systems\, and studying the associated orbit equivalence rela tions has been the subject of a lot of study over many years. In this talk we will consider some natural constructions and discuss classification re sults for such equivalence relations. In particular\, we will study how th e behavior of certain central sequences implies structural results on the involved equivalence relations and their products. All necessary notions w ill be introduced during the talk. This is partially based on joint work w ith Adrian Ioana.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Haydar Göral (İzmir Institute of Technology) DTSTART:20211109T113000Z DTEND:20211109T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/2 DESCRIPTION:Title: Classification of Quadratic Number Fields Using Diophanti ne Equations\nby Haydar Göral (İzmir Institute of Technology) as par t of Koç University Mathematics Seminar\n\n\nAbstract\nIn this talk\, we consider some Diophantine equations over number fields. Recall that a numb er field is a finite field extension of the field of rational numbers. We show that the finiteness of the set of all solutions of certain Diophantin e equations determines quadratic number fields among all number fields. Al ong the way\, we explain our motivation\, we give many examples and relate the results to nonstandard analysis and arithmetic geometry.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Or Shalom (Einstein Institute of Mathematics) DTSTART:20211123T113000Z DTEND:20211123T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/3 DESCRIPTION:Title: A structure theorem for Gowers-Host-Kra seminorms for non -finitely generated countable abelian groups of unbounded torsion\nby Or Shalom (Einstein Institute of Mathematics) as part of Koç University M athematics Seminar\n\n\nAbstract\nFurstenberg's famous proof of Szemeredi' s theorem leads to a natural question about the convergence and limit of s ome multiple ergodic averages. In the case of $\\mathbb{Z}$-actions these averages were studied by Host-Kra and Ziegler. They show that the limiting behavior of such multiple ergodic average is determined on a certain fact or that can be given the structure of an inverse limit of nilsystems (i.e. rotations on a nilmanifold). This structure result can be generalized to $\\mathbb{Z}^d$-actions (where the average is taken over a Folner sequence )\, but the non-finitely generated case is still open. The only progress p rior to our work is due to Bergelson Tao and Ziegler\, who studied actions of the infinite direct sum $\\mathbb{Z}/p\\mathbb{Z}$. In our work we gen eralize this further to the case where the sum is taken over different pri mes (the most interesting case is when the multiset of primes is unbounded ). We will explain how this case is significantly different from the work of Bergelson Tao and Ziegler by describing a new phenomenon that only happ ens in these settings. Moreover\, we will discuss a generalized version of nilsystems that plays a role in our work and some corollaries. If time al lows we will also discuss the group actions of other abelian groups.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Özge Ülkem (Galatasaray University) DTSTART:20211130T113000Z DTEND:20211130T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/4 DESCRIPTION:Title: Generalized D-elliptic sheaves and their moduli space \nby Özge Ülkem (Galatasaray University) as part of Koç University Math ematics Seminar\n\n\nAbstract\nElliptic curves play a fundamental role in algebraic number theory. In the 1970’s\nDrinfeld defined analogues of el liptic curves in the function field setting\, which are\nnow called Drinfe ld modules. Later on he defined a categorically equivalent notion\,\ncalle d elliptic sheaves\, and studied their moduli space to prove Langlands cor respondence. Since then many generalizations of Drinfeld modules and ellip tic sheaves have been worked out. In the first part of this talk we will f orm the function field and classical setting and discuss similarities betw een them. Then\, we define Drinfeld\nmodules\, discuss the analogy between elliptic curves and Drinfeld modules. In the\nsecond part we will define a new generalization of elliptic sheaves\, called generalized\nD-elliptic sheaves and talk on their moduli space and of the uniformization of the\nl atter if time permits.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART:20211207T130000Z DTEND:20211207T141000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/5 DESCRIPTION:Title: Isolated Points on Modular Curves\nby Özlem Ejder (B oğaziçi University) as part of Koç University Mathematics Seminar\n\n\n Abstract\nOne of the oldest areas of mathematics is the study of integer o r 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 inf inite. This can be determined by the genus of the curve defined by such eq uations. In particular\, if the genus is greater than one\, there are fini tely many rational points on a curve. \n\nWhat 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 ca ll such solutions of degree 2\,3 or d in general. In this talk\, we will d iscuss when a curve has infinitely many degree d points focusing particula rly on points on modular curves.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Luka Milićević (Mathematical Institute of the Serbian Academy of Sciences and Arts) DTSTART:20211214T113000Z DTEND:20211214T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/6 DESCRIPTION:Title: Bilinear Bogolyubov Argument in Abelian Groups\nby Lu ka Milićević (Mathematical Institute of the Serbian Academy of Sciences and Arts) as part of Koç University Mathematics Seminar\n\n\nAbstract\nBi linear Bogolyubov argument states that if we start with a dense set $A$ of \na product $U\\times V$ of finite vector spaces and carry out sufficientl y many\nsteps where we replace every row or every column of $A$ by the set \ndifference of it with itself\, then inside the resulting set we obtain a \nbilinear variety of codimension bounded in terms of the density of $A$. In\nthis talk\, we focus on a generalization of this theorem to arbitrary\ nfinite abelian groups. Along the way we also discuss analogues of a few\n linear-algebraic facts as well as quasirandomness of analogues of bilinear \nvarieties in the setting of finite abelian groups.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Faruk Temur (İzmir Institute of Technology) DTSTART:20211221T113000Z DTEND:20211221T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/7 DESCRIPTION:Title: Discrete fractional integrals\, lattice points on thin ar cs\, and diophantine approximation\nby Faruk Temur (İzmir Institute o f Technology) as part of Koç University Mathematics Seminar\n\n\nAbstract \nThe study of discrete fractional integral operators began with an articl e of Arkhipov and Oskolkov on boundedness of certain multipliers\, and for over thirty years concentrated on cases with translation invariant or qua sitranslation invariant phase polynomial\, as these cases are amenable to the Fourier transform and the Hardy-Littlewood circle method. Recently in joint work with E. Sert\, we introduced methods from arithmetic to study d iscrete fractional integral operators along quadratic bivariate polynomial s in their full generality. This is achieved by combining the information regarding distribution of lattice points on conics gleaned via classical t heory of binary quadratic forms and sieving with very careful partitioning of sums under question. This effort as a side benefit yields new results on various conjectures on concentration of lattice points on conics and ma kes connections to diophantine approximation. \n\n\nIn this talk we will g ive a brief summary of these results on fractional integrals and lattice p oints\, together with their mathematical context and main ideas of their p roofs.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Önder Türk (Institute of Applied Mathematics at METU) DTSTART:20220104T130000Z DTEND:20220104T141000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/8 DESCRIPTION:Title: Modal analysis of linear elasticity equations in the inco mpressible limit\nby Önder Türk (Institute of Applied Mathematics at METU) as part of Koç University Mathematics Seminar\n\n\nAbstract\nA mod al analysis approach for approximating the linear elasticity equations wit h the incompressibility constraint will be presented. The spectrum of the linear elasticity operator is approximated\nusing an optimally convergent stabilized finite element method that is based on a variational multiscale approach. The convergence of the approximate solutions to the true ones i n appropriate norms is proved both theoretically and numerically.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Oğuz Şavk (Boğaziçi University) DTSTART:20211228T113000Z DTEND:20211228T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/9 DESCRIPTION:Title: Homology 3-spheres bounding contractible 4-manifolds and homology 4-balls\nby Oğuz Şavk (Boğaziçi University) as part of Ko ç University Mathematics Seminar\n\n\nAbstract\nA central problem in low- dimensional topology asks which homology 3-spheres bound contractible 4-ma nifolds and homology 4-balls. In this talk\, we address this problem for p lumbed 3-manifolds and we\npresent the classical and new results. Our appr oach is based on Mazur’s famous argument and its generalization\, they t ogether provide a unification of all recognized results.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Fritz (University of Innsbruck) DTSTART:20220419T113000Z DTEND:20220419T124000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/10 DESCRIPTION:Title: Categorical probability and the de Finetti theorem\n by Tobias Fritz (University of Innsbruck) as part of Koç University Mathe matics Seminar\n\n\nAbstract\nProbability theory and statistics are usuall y developed based on Kolmogorov’s axioms of probability space as a found ation. In this talk\, I will present an alternative foundation that is cur rently under development\, and I will argue that it improves over the trad itional one in various respects. This approach is formulated in terms of c ategory theory\, and it makes Markov kernels instead of probability spaces into the fundamental primitives. Its abstract nature also implies that no measure theory is needed. After introducing the approach itself\, I will summarize our proof of the de Finetti theorem in terms of it.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Seregin (Oxford University) DTSTART:20220621T113000Z DTEND:20220621T130000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/11 DESCRIPTION:Title: Axisymmetric Solutions to the Navier-Stokes Equations\nby Gregory Seregin (Oxford University) as part of Koç University Mathe matics Seminar\n\nLecture held in SCI 103.\n\nAbstract\nI’ll discuss rec ent regularity results for axisymmetric solutions to the Navier-Stokes equ ations. Among them are slightly supercritical assumptions providing smooth ness\, which\, for example\, exclude Type I blowups of axisymmetric soluti ons.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Donoso (University of Chile) DTSTART:20220628T113000Z DTEND:20220628T130000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/12 DESCRIPTION:Title: Multiplicative actions and applications\nby Sebastia n Donoso (University of Chile) as part of Koç University Mathematics Semi nar\n\nLecture held in SCI 103.\n\nAbstract\nIn this talk\, I will discuss recurrence problems for actions of the multiplicative semigroup of intege rs. Answers to these problems have consequences in number theory and comb inatorics\, such as understanding whether Pythagorean trios are partition regular. I will present in general terms the questions\, strategies from d ynamics to address them and mention some recent results we obtained. This is joint work with Anh Le\, Joel Moreira\, and Wenbo Sun.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Henrik Kreidler (University of Wuppertal) DTSTART:20220726T113000Z DTEND:20220726T123000Z DTSTAMP:20260424T095340Z UID:kocuniversitymathseminar/13 DESCRIPTION:Title: Pure Koopmanism: An operator theoretic approach to dynam ical systems\nby Henrik Kreidler (University of Wuppertal) as part of Koç University Mathematics Seminar\n\nLecture held in SCI 103\, Koc main campus.\n\nAbstract\nDynamical systems play a key role in modern mathemati cs and come in many variations\, e.g.\, in the form of continuous transfor mations on topological spaces or measure-preserving maps on probability sp aces. In this talk we discuss a simple\, but effective operator theoretic approach to such systems known as the Koopman linearization.\n LOCATION:https://researchseminars.org/talk/kocuniversitymathseminar/13/ END:VEVENT END:VCALENDAR