BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shahar Mozes DTSTART:20210809T111000Z DTEND:20210809T114000Z DTSTAMP:20260416T222520Z UID:MSR80/1 DESCRIPTION:Title: Su rface subgroups in uniform lattices of some semisimple Lie groups\nby Shahar Mozes as part of International Conference on Discrete groups\, Geom etry and Arithmetic\n\n\nAbstract\nIt is proved that any uniform lattice i n a simple complex Lie group G contains\na surface group. This theorem is a generalization of the celebrated Kahn-Markovic Theorem which\ndeals with the case of G=PSL(2\, C). [This is joint work with Jeremy Kahn and Franco is Labourie.]\n LOCATION:https://researchseminars.org/talk/MSR80/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tsachik Gelander DTSTART:20210809T115000Z DTEND:20210809T122000Z DTSTAMP:20260416T222520Z UID:MSR80/2 DESCRIPTION:Title: In finite volume and infinite injectivity radius\nby Tsachik Gelander as part of International Conference on Discrete groups\, Geometry and Arithme tic\n\n\nAbstract\nWe prove the following conjecture of Margulis. Let G be a higher rank simple Lie group\nand Λ a discrete subgroup. Then vol(G/Λ ) is finite if and only if there is a compact set in G which\nintersects n ontrivially every conjugate of Λ. In the special case where Λ is a norma l subgroup of a\nlattice this is the celebrated normal subgroup theorem of Margulis. [This is joint work with Mikolaj\nFraczyk.]\n LOCATION:https://researchseminars.org/talk/MSR80/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Zalesski DTSTART:20210809T130000Z DTEND:20210809T133000Z DTSTAMP:20260416T222520Z UID:MSR80/3 DESCRIPTION:Title: Th e congruence subgroup problem: rank one case\nby Pavel Zalesski as par t of International Conference on Discrete groups\, Geometry and Arithmetic \n\n\nAbstract\nAfter reviewing the basic definitions pertaining to the co ngruence subgroup problem\nfor algebraic groups\, we will discuss the avai lable results concerning the structure of the\ncongruence kernel in the ra nk one case.\n LOCATION:https://researchseminars.org/talk/MSR80/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Rapinchuk DTSTART:20210809T134000Z DTEND:20210809T141000Z DTSTAMP:20260416T222520Z UID:MSR80/4 DESCRIPTION:Title: Al gebraic groups with good reduction\nby Igor Rapinchuk as part of Inter national Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbst ract\nTechniques involving reduction are very common in number theory and arithmetic\ngeometry. In particular\, elliptic curves and general abelian varieties having good reduction have\nbeen the subject of very intensive i nvestigations over the years. The purpose of this talk is to\nreport on re cent work that focuses on good reduction in the context of reductive linea r algebraic\ngroups over finitely generated fields. [Parts of this work ar e joint with V. Chernousov and A.\nRapinchuk.]\n LOCATION:https://researchseminars.org/talk/MSR80/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Chernousov DTSTART:20210809T142000Z DTEND:20210809T145000Z DTSTAMP:20260416T222520Z UID:MSR80/5 DESCRIPTION:Title: On conjugacy of Cartan subalgebras in extended affine Lie algebras and class ification of torsors over Laurent polynomial rings\nby Vladimir Cherno usov as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nThe conjugacy of split Cartan subalgebras in th e finite-dimensional simple Lie algebras\n(Chevalley theorem) and in the s ymmetrizable Kac-Moody Lie algebras (Peterson-Kac theorem) are\nfundamenta l results of the theory of Lie algebras. In this talk we will discuss how the problem of\nconjugacy for a class of Lie algebras called extended affi ne Lie algebras (that are in a precise sense\nhigher nullity analogues of the affine Kac-Moody Lie algebras) interwind with the classification of\nt orsors of reductive group schemes over Laurent polynomial rings.\n LOCATION:https://researchseminars.org/talk/MSR80/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Hee Oh DTSTART:20210810T103000Z DTEND:20210810T110000Z DTSTAMP:20260416T222520Z UID:MSR80/6 DESCRIPTION:Title: Un ipotent flows on homogeneous spaces of infinite volume\nby Hee Oh as p art of International Conference on Discrete groups\, Geometry and Arithmet ic\n\n\nAbstract\nM. S. Raghunathan conjectured around 1980 that in a homo geneous space of a Lie group\nG\, with finite volume\, any orbit closure o f a connected subgroup of G generated by unipotent\nelements is homogeneou s. This conjecture was settled by M. Ratner around 1990. Looking for\nanal ogues of Ratner's theorem in the infinite volume setting is a major challe nge. For any n>2\, we\npresent a family of homogeneous spaces of SO(n\,1)\ , with infinite volume\, in which we classify all\npossible orbit closures of any connected subgroup generated by unipotent elements. [This talk is\ nbased on joint works with McMullen and Mohammadi (for n=3) and with Minju Lee (for n>3)].\n LOCATION:https://researchseminars.org/talk/MSR80/6/ END:VEVENT BEGIN:VEVENT SUMMARY:M.M. Radhika DTSTART:20210810T111000Z DTEND:20210810T114000Z DTSTAMP:20260416T222520Z UID:MSR80/7 DESCRIPTION:Title: Th e Congruence Subgroup Problem for groups of inner type A_n\nby M.M. Ra dhika as part of International Conference on Discrete groups\, Geometry an d Arithmetic\n\n\nAbstract\nThis talk will comprise of a short introductio n to the Congruence subgroup problem as\nreformulated by Serre\, a review of the developments of the problem for groups of inner type A_n\nand an ap proach for tackling the problem in a specific case. [Talk based on joint w ork with M. S.\nRaghunathan.]\n LOCATION:https://researchseminars.org/talk/MSR80/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai-Uwe Bux DTSTART:20210810T115000Z DTEND:20210810T122000Z DTSTAMP:20260416T222520Z UID:MSR80/8 DESCRIPTION:Title: An alternative construction for the bordification of outer space\nby Kai -Uwe Bux as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nThe Bestvina-Feighn bordification of outer space is analogous to the Borel-Serre\nbordification. We describe a differ ent construction for a homeomorphic space that is the analogue\nof Grayson 's equivariant deformation retract of the symmetric space. The alternative construction\nsimplifies the analysis of connectivity properties and ther eby also the proof that the group of outer\nautomorphisms of a free group is a virtual duality group. [This is joint work with Peter Smillie and\nKa ren Vogtmann.]\n LOCATION:https://researchseminars.org/talk/MSR80/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Raman Parimala DTSTART:20210810T130000Z DTEND:20210810T133000Z DTSTAMP:20260416T222520Z UID:MSR80/9 DESCRIPTION:Title: Ha sse principle for simply connected groups\nby Raman Parimala as part o f International Conference on Discrete groups\, Geometry and Arithmetic\n\ n\nAbstract\nHasse principle for the isotropy of quadratic forms over numb er fields is the classical\ntheorem of Hasse-Minkowski. We describe Kneser 's conjectures on Hasse principle for simply\nconnected groups over number fields and a conjecture of Serre in the general context of\ncohomological dimension 2 fields placing Kneser's conjecture in a very general context. We then\ndescribe questions and conjectures for function fields of curves over p-adic and number fields and\nsome progress in this direction.\n LOCATION:https://researchseminars.org/talk/MSR80/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Goldman DTSTART:20210810T134000Z DTEND:20210810T141000Z DTSTAMP:20260416T222520Z UID:MSR80/10 DESCRIPTION:Title: D ynamics and the classification of geometries on surfaces\nby Bill Gold man as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nMany interesting dynamical systems arise from th e classification of locally homogeneous\ngeometric structures and flat con nections on manifolds. Their classification mimics that of\nRiemann surfac es by the Riemann moduli space\, which identifies as the quotient of Teich mueller\nspace of marked Riemann surfaces by the action of the mapping cla ss group. However\, unlike\nRiemann surfaces\, these actions are generally chaotic. A striking elementary example is Baues's\ntheorem that the defor mation space of complete affine structures on the 2-torus is the plane wit h\nthe usual linear action of GL(2\,Z) (the mapping class group of the tor us). We discuss specific\nexamples of these dynamics for some simple surfa ces\, where the relative character varieties\nappear as cubic surfaces in affine 3-space. Complicated dynamics seems to accompany\ncomplicated topol ogies\, which we interpret as (possibly singular) hyperbolic structures on \nsurfaces.\n LOCATION:https://researchseminars.org/talk/MSR80/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David M. Fisher DTSTART:20210810T142000Z DTEND:20210810T145000Z DTSTAMP:20260416T222520Z UID:MSR80/11 DESCRIPTION:Title: A rithmeticity\, superrigidity and totally geodesic manifolds\nby David M. Fisher as part of International Conference on Discrete groups\, Geometr y and Arithmetic\n\n\nAbstract\nI will discuss recent results showing that a finite volume real or complex hyperbolic\nmanifold with infinitely many maximal totally geodesic submanifolds is arithmetic. The proof\nbrings to gether homogeneous dynamics and a new superrigidity theorem. [This is join t work with\nBader\, Miller and Stover.]\n LOCATION:https://researchseminars.org/talk/MSR80/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Louis Colliot-Thélène DTSTART:20210811T103000Z DTEND:20210811T110000Z DTSTAMP:20260416T222520Z UID:MSR80/12 DESCRIPTION:Title: O n the local-global principle for reductive groups over semi-global fields< /a>\nby Jean-Louis Colliot-Thélène as part of International Conference o n Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nBy semi-global field\, we mean the field of rational functions of a curve over the field of\nfractions of a complete discrete valuation ring. Such a semi-global fi eld may be completed in\nvarious ways. Over the last ten years\, the valid ity of a Hasse principle for principal homogeneous\nspaces of reductive gr oups over semi-global fields has been investigated. I shall report on this . In\nparticular we shall see that in this context the principle need not hold for semisimple simply connected groups\, whereas it holds for reducti ve groups whose underlying variety is birational to\naffine space. [This i s joint work with D. Harbater\, J. Hartmann\, D. Krashen\, R. Parimala and V.\nSuresh.]\n LOCATION:https://researchseminars.org/talk/MSR80/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Umberto Zannier DTSTART:20210811T111000Z DTEND:20210811T114000Z DTSTAMP:20260416T222520Z UID:MSR80/13 DESCRIPTION:Title: B ounded generation in anisotropic linear group\nby Umberto Zannier as p art of International Conference on Discrete groups\, Geometry and Arithmet ic\n\n\nAbstract\nUsing Diophantine results from the theory of integral po ints in multiplicative tori\, we\ncharacterize anisotropic linear groups i n characteristic 0 having bounded generation. (Joint work\nwith P. Corvaja \, J. Ren and A. Rapinchuk.)\n LOCATION:https://researchseminars.org/talk/MSR80/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Breuillard DTSTART:20210811T115000Z DTEND:20210811T122000Z DTSTAMP:20260416T222520Z UID:MSR80/14 DESCRIPTION:Title: A pproximate lattices and quasi-crystals\nby Emmanuel Breuillard as part of International Conference on Discrete groups\, Geometry and Arithmetic\ n\n\nAbstract\nAperiodic tilings of the plane such as the Penrose tiling a re instances of discrete\napproximate subgroups of R^2. These Euclidean qu asi-crystals were studied by Yves Meyer in the\nseventies and proved to ar ise from periodic tilings of a bigger space by the familiar cut-and-projec t\nconstruction. In this talk I will discuss tilings of other non-Euclidea n geometries\, especially those\narising from symmetric spaces of non-comp act type. In this talk I will survey recent advances\nestablishing super-r igidity and arithmeticity theorems for approximate lattices that directly\ ngeneralize the Mostow-Margulis theorems.\n LOCATION:https://researchseminars.org/talk/MSR80/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nimish Shah DTSTART:20210811T134000Z DTEND:20210811T141000Z DTSTAMP:20260416T222520Z UID:MSR80/16 DESCRIPTION:Title: S harp conditions for equidistribution of translates of a subspace of a horo sphere by a diagonal flow in the space of unimodular lattices\nby Nimi sh Shah as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nWe consider the action of the one-parameter subgroup $a(t) = \\text{exp}((n-1)t\, -t\, \\ldots\, -t)$ of\nSL(n\,R) on the space X of unimodular lattices in $R^n$. Let C be an analytic curve on the expanding\nhorosphere of a(t) in X through the standard lattice $Z^n$ . Let μ be a smooth probability measure on\nC. We describe necessary and sufficient conditions\, in terms of Diophantine approximation and\nalgebra ic number fields\, on the smallest affine subspace containing C so that th e translated\nmeasures a(t)μ get equidistributed in X as $t \\rightarrow \\infty$. This generalizes my earlier result showing equidistribution of t ranslates of curves not contained in proper affine subspaces. The result a nswers a question of Davenport and Schmidt on non-improvability of Dirichl et’s approximation.\n[The case of n = 3 is a joint work with D. Kleinboc k\, N. DeSaxe\, and P. Yang\; and the general case is a joint work with P. Yang.]\n LOCATION:https://researchseminars.org/talk/MSR80/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Amir Mohammadi DTSTART:20210811T142000Z DTEND:20210811T145000Z DTSTAMP:20260416T222520Z UID:MSR80/17 DESCRIPTION:Title: E ffective results in homogeneous dynamics\nby Amir Mohammadi as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n \nAbstract\nRigidity phenomena in homogeneous dynamics have been extensive ly studied over the\npast few decades with several striking results and ap plications. In this talk\, we will give an overview\nof recent activities related to finitary analysis in this context.\n LOCATION:https://researchseminars.org/talk/MSR80/17/ END:VEVENT BEGIN:VEVENT SUMMARY:S. G. Dani DTSTART:20210811T150000Z DTEND:20210811T160000Z DTSTAMP:20260416T222520Z UID:MSR80/18 DESCRIPTION:Title: F elicitation of M. S. Raghunathan\nby S. G. Dani as part of Internation al Conference on Discrete groups\, Geometry and Arithmetic\n\nAbstract: TB A\n LOCATION:https://researchseminars.org/talk/MSR80/18/ END:VEVENT END:VCALENDAR