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:20260404T111326Z UID:kocuniversitymathseminar/1 DESCRIPTION:Title: Group actions and equivalence relations\nby Pi eter Spaas (UCLA) as part of Koç University Mathematics Seminar\n\n\nAbst ract\nGroup actions of a countable group on a measure space give rise to i nteresting dynamical systems\, and studying the associated orbit equivalen ce relations has been the subject of a lot of study over many years. In th is talk we will consider some natural constructions and discuss classifica tion results for such equivalence relations. In particular\, we will study how the behavior of certain central sequences implies structural results on the involved equivalence relations and their products. All necessary no tions will be introduced during the talk. This is partially based on joint work with Adrian Ioana.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /1/ END:VEVENT BEGIN:VEVENT SUMMARY:Haydar Göral (İzmir Institute of Technology) DTSTART:20211109T113000Z DTEND:20211109T124000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/2 DESCRIPTION:Title: Classification of Quadratic Number Fields Using Di ophantine Equations\nby Haydar Göral (İzmir Institute of Technology) as part of Koç University Mathematics Seminar\n\n\nAbstract\nIn this tal k\, we consider some Diophantine equations over number fields. Recall that a number field is a finite field extension of the field of rational numbe rs. We show that the finiteness of the set of all solutions of certain Dio phantine equations determines quadratic number fields among all number fie lds. Along the way\, we explain our motivation\, we give many examples and relate the results to nonstandard analysis and arithmetic geometry.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /2/ END:VEVENT BEGIN:VEVENT SUMMARY:Or Shalom (Einstein Institute of Mathematics) DTSTART:20211123T113000Z DTEND:20211123T124000Z DTSTAMP:20260404T111326Z 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 Unive rsity Mathematics Seminar\n\n\nAbstract\nFurstenberg's famous proof of Sze meredi's theorem leads to a natural question about the convergence and lim it of some multiple ergodic averages. In the case of $\\mathbb{Z}$-actions these averages were studied by Host-Kra and Ziegler. They show that the l imiting behavior of such multiple ergodic average is determined on a certa in factor that can be given the structure of an inverse limit of nilsystem s (i.e. rotations on a nilmanifold). This structure result can be generali zed to $\\mathbb{Z}^d$-actions (where the average is taken over a Folner s equence)\, but the non-finitely generated case is still open. The only pro gress prior 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 generalize this further to the case where the sum is taken over differ ent primes (the most interesting case is when the multiset of primes is un bounded). We will explain how this case is significantly different from th e work of Bergelson Tao and Ziegler by describing a new phenomenon that on ly happens in these settings. Moreover\, we will discuss a generalized ver sion of nilsystems that plays a role in our work and some corollaries. If time allows we will also discuss the group actions of other abelian groups .\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /3/ END:VEVENT BEGIN:VEVENT SUMMARY:Özge Ülkem (Galatasaray University) DTSTART:20211130T113000Z DTEND:20211130T124000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/4 DESCRIPTION:Title: Generalized D-elliptic sheaves and their moduli sp ace\nby Özge Ülkem (Galatasaray University) as part of Koç Universi ty Mathematics Seminar\n\n\nAbstract\nElliptic curves play a fundamental r ole in algebraic number theory. In the 1970’s\nDrinfeld defined analogue s of elliptic curves in the function field setting\, which are\nnow called Drinfeld modules. Later on he defined a categorically equivalent notion\, \ncalled elliptic sheaves\, and studied their moduli space to prove Langla nds correspondence. Since then many generalizations of Drinfeld modules an d elliptic sheaves have been worked out. In the first part of this talk we will form the function field and classical setting and discuss similariti es between 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-el liptic sheaves and talk on their moduli space and of the uniformization of the\nlatter if time permits.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /4/ END:VEVENT BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART:20211207T130000Z DTEND:20211207T141000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/5 DESCRIPTION:Title: Isolated Points on Modular Curves\nby Özlem E jder (Boğaziçi University) as part of Koç University Mathematics Semina r\n\n\nAbstract\nOne of the oldest areas of mathematics is the study of in teger or rational solutions to polynomial equations with integer coefficie nts 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 a re finitely many rational points on a curve. \n\nWhat happens when one all ows for solutions involving square-roots of integers or cubic roots? Perh aps 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 pa rticularly on points on modular curves.\n LOCATION:https://stable.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:20260404T111326Z UID:kocuniversitymathseminar/6 DESCRIPTION:Title: Bilinear Bogolyubov Argument in Abelian Groups \nby Luka Milićević (Mathematical Institute of the Serbian Academy of Sc iences and Arts) as part of Koç University Mathematics Seminar\n\n\nAbstr act\nBilinear 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 suff iciently 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 o btain a\nbilinear variety of codimension bounded in terms of the density o f $A$. In\nthis talk\, we focus on a generalization of this theorem to arb itrary\nfinite abelian groups. Along the way we also discuss analogues of a few\nlinear-algebraic facts as well as quasirandomness of analogues of b ilinear\nvarieties in the setting of finite abelian groups.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /6/ END:VEVENT BEGIN:VEVENT SUMMARY:Faruk Temur (İzmir Institute of Technology) DTSTART:20211221T113000Z DTEND:20211221T124000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/7 DESCRIPTION:Title: Discrete fractional integrals\, lattice points on thin arcs\, and diophantine approximation\nby Faruk Temur (İzmir Inst itute of Technology) as part of Koç University Mathematics Seminar\n\n\nA bstract\nThe study of discrete fractional integral operators began with an article of Arkhipov and Oskolkov on boundedness of certain multipliers\, and for over thirty years concentrated on cases with translation invariant or quasitranslation invariant phase polynomial\, as these cases are amena ble to the Fourier transform and the Hardy-Littlewood circle method. Recen tly in joint work with E. Sert\, we introduced methods from arithmetic to study discrete fractional integral operators along quadratic bivariate pol ynomials in their full generality. This is achieved by combining the infor mation regarding distribution of lattice points on conics gleaned via clas sical theory of binary quadratic forms and sieving with very careful parti tioning of sums under question. This effort as a side benefit yields new r esults on various conjectures on concentration of lattice points on conics and makes connections to diophantine approximation. \n\n\nIn this talk we will give a brief summary of these results on fractional integrals and la ttice points\, together with their mathematical context and main ideas of their proofs.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /7/ END:VEVENT BEGIN:VEVENT SUMMARY:Önder Türk (Institute of Applied Mathematics at METU) DTSTART:20220104T130000Z DTEND:20220104T141000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/8 DESCRIPTION:Title: Modal analysis of linear elasticity equations in t he incompressible limit\nby Önder Türk (Institute of Applied Mathema tics at METU) as part of Koç University Mathematics Seminar\n\n\nAbstract \nA modal analysis approach for approximating the linear elasticity equati ons with the incompressibility constraint will be presented. The spectrum of the linear elasticity operator is approximated\nusing an optimally conv ergent stabilized finite element method that is based on a variational mul tiscale approach. The convergence of the approximate solutions to the true ones in appropriate norms is proved both theoretically and numerically.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /8/ END:VEVENT BEGIN:VEVENT SUMMARY:Oğuz Şavk (Boğaziçi University) DTSTART:20211228T113000Z DTEND:20211228T124000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/9 DESCRIPTION:Title: Homology 3-spheres bounding contractible 4-manifol ds and homology 4-balls\nby Oğuz Şavk (Boğaziçi University) as par t of Koç University Mathematics Seminar\n\n\nAbstract\nA central problem in low-dimensional topology asks which homology 3-spheres bound contractib le 4-manifolds and homology 4-balls. In this talk\, we address this proble m for plumbed 3-manifolds and we\npresent the classical and new results. O ur approach is based on Mazur’s famous argument and its generalization\, they together provide a unification of all recognized results.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Fritz (University of Innsbruck) DTSTART:20220419T113000Z DTEND:20220419T124000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/10 DESCRIPTION:Title: Categorical probability and the de Finetti theore m\nby Tobias Fritz (University of Innsbruck) as part of Koç Universit y Mathematics Seminar\n\n\nAbstract\nProbability theory and statistics are usually developed based on Kolmogorov’s axioms of probability space as a foundation. In this talk\, I will present an alternative foundation that is currently under development\, and I will argue that it improves over t he traditional one in various respects. This approach is formulated in ter ms of category 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://stable.researchseminars.org/talk/kocuniversitymathseminar /10/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Seregin (Oxford University) DTSTART:20220621T113000Z DTEND:20220621T130000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/11 DESCRIPTION:Title: Axisymmetric Solutions to the Navier-Stokes Equat ions\nby Gregory Seregin (Oxford University) as part of Koç Universit y Mathematics Seminar\n\nLecture held in SCI 103.\n\nAbstract\nI’ll disc uss recent regularity results for axisymmetric solutions to the Navier-Sto kes equations. Among them are slightly supercritical assumptions providing smoothness\, which\, for example\, exclude Type I blowups of axisymmetric solutions.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Donoso (University of Chile) DTSTART:20220628T113000Z DTEND:20220628T130000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/12 DESCRIPTION:Title: Multiplicative actions and applications\nby S ebastian Donoso (University of Chile) as part of Koç University Mathemati cs Seminar\n\nLecture held in SCI 103.\n\nAbstract\nIn this talk\, I will discuss recurrence problems for actions of the multiplicative semigroup of integers. Answers to these problems have consequences in number theory a nd combinatorics\, such as understanding whether Pythagorean trios are par tition regular. I will present in general terms the questions\, strategies from dynamics 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://stable.researchseminars.org/talk/kocuniversitymathseminar /12/ END:VEVENT BEGIN:VEVENT SUMMARY:Henrik Kreidler (University of Wuppertal) DTSTART:20220726T113000Z DTEND:20220726T123000Z DTSTAMP:20260404T111326Z UID:kocuniversitymathseminar/13 DESCRIPTION:Title: Pure Koopmanism: An operator theoretic approach t o dynamical systems\nby Henrik Kreidler (University of Wuppertal) as p art of Koç University Mathematics Seminar\n\nLecture held in SCI 103\, Ko c main campus.\n\nAbstract\nDynamical systems play a key role in modern ma thematics and come in many variations\, e.g.\, in the form of continuous t ransformations on topological spaces or measure-preserving maps on probabi lity spaces. In this talk we discuss a simple\, but effective operator the oretic approach to such systems known as the Koopman linearization.\n LOCATION:https://stable.researchseminars.org/talk/kocuniversitymathseminar /13/ END:VEVENT END:VCALENDAR