BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Lubotzky (The Hebrew University of Jerusalem) DTSTART:20211005T150000Z DTEND:20211005T163000Z DTSTAMP:20260422T212936Z UID:Vinberg/1 DESCRIPTION:Title: Stability and testability of permutations' equations\nby Alex Lubotzky (The Hebrew University of Jerusalem) as part of The Vinberg Lecture Serie s\n\n\nAbstract\nLet $A$ and $B$ be two permutations in $\\text{Sym}(n)$ t hat ``almost commute'' -- are they a small deformation of permutations tha t truly commute? More generally\, if $R$ is a system of words-equations in variables $X = \\{x_1\, \\ldots \,x_d\\}$ and $A_1\, \\ldots \,A_d$ are p ermutations that are nearly solutions\; are they near true solutions? \n\n It turns out that the answer to this question depends only on the group pr esented by the generators $X$ and relations $R$. This leads to the notions of ``stable groups'' and ``testable groups''. \n\nWe will present a few r esults and methods which were developed in recent years to check whether a group is stable or testable. We will also describe the connection of this subject with property testing in computer science\, with the long-standin g problem of whether every group is sofic\, and with invariant random subg roups.\n LOCATION:https://researchseminars.org/talk/Vinberg/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Reid (Rice University\, USA) DTSTART:20211019T150000Z DTEND:20211019T163000Z DTSTAMP:20260422T212936Z UID:Vinberg/2 DESCRIPTION:Title: The geometry and topology of arithmetic hyperbolic manifolds of simplest t ype\nby Alan Reid (Rice University\, USA) as part of The Vinberg Lectu re Series\n\n\nAbstract\nThis talk will survey as well as discuss geometri c and topological properties of arithmetic hyperbolic manifolds of simples t type. These are precisely the class of arithmetic hyperbolic manifolds t hat contain an immersed co-dimension one totally geodesic submanifolds.\n LOCATION:https://researchseminars.org/talk/Vinberg/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Alekseevsky (IITP RAS\, Moscow\, Russia) DTSTART:20211123T150000Z DTEND:20211123T163000Z DTSTAMP:20260422T212936Z UID:Vinberg/4 DESCRIPTION:Title: Special Vinberg cones and their application to Supergravity\nby Dmitry Alekseevsky (IITP RAS\, Moscow\, Russia) as part of The Vinberg Lecture S eries\n\n\nAbstract\nIn the early 1960s\, Vinberg gave a description of ho mogeneous convex cones as cones of Hermitian positive definite matrices in a matrix $T$-algebra $M_n$ of $(n\\times n)$-matrices whose diagonal entr ies are just real numbers\, but off-diagonal elements belong to different vector spaces. It turns out that rank 3 special Vinberg cones (correspondi ng to Clifford algebras) have important applications to Supergravity. No s pecial background is required. The talk is based on joint works with V. Co rtes\; and with A. Marrani and A. Spiro.\n LOCATION:https://researchseminars.org/talk/Vinberg/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Sarnak (IAS Princeton\, USA) DTSTART:20211130T150000Z DTEND:20211130T163000Z DTSTAMP:20260422T212936Z UID:Vinberg/5 DESCRIPTION:Title: Reflection groups and monodromy\nby Peter Sarnak (IAS Princeton\, USA) as part of The Vinberg Lecture Series\n\n\nAbstract\nVinberg's theory of reflection groups has wide applications. We discuss some of these\, to mon odromy groups of hypergeometric and Painlevé equations. The nonlinear cas e is intimately connected to affine Markoff surfaces and it is a central i ngredient in the Diophantine analysis of these surfaces.\n LOCATION:https://researchseminars.org/talk/Vinberg/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Maryna Viazovska (EPF Lausanne\, Switzerland) DTSTART:20211207T150000Z DTEND:20211207T163000Z DTSTAMP:20260422T212936Z UID:Vinberg/6 DESCRIPTION:Title: The sphere packing problem\nby Maryna Viazovska (EPF Lausanne\, Switze rland) as part of The Vinberg Lecture Series\n\n\nAbstract\nThe sphere pac king problem asks for the densest configuration of non-overlapping unit ba lls in space. In this talk I shall speak about the sphere packing problem in various spaces and its generalisations. The talk will focus on linear p rogramming and semidefinite programming methods as powerful tools for anal ysing and\, in some cases\, completely solving geometric optimisation ques tions.\n LOCATION:https://researchseminars.org/talk/Vinberg/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Bjorn Poonen (MIT) DTSTART:20220126T153000Z DTEND:20220126T170000Z DTSTAMP:20260422T212936Z UID:Vinberg/8 DESCRIPTION:Title: Undecidability in number theory\nby Bjorn Poonen (MIT) as part of The Vinberg Lecture Series\n\n\nAbstract\nHilbert's tenth problem asked for an algorithm that\, given a\nmultivariable polynomial equation with integer coefficients\, would\ndecide whether there exists a solution in integers. Around 1970\,\nMatiyasevich\, building on earlier work of Davis\, Putnam\ , and Robinson\,\nshowed that no such algorithm exists. But the answer to the analogous\nquestion with integers replaced by rational numbers is sti ll unknown\,\nand there is not even agreement among experts as to what the answer\nshould be. The second half of the lecture will explore some of t he\ntechniques from arithmetic geometry that have been used towards\nanswe ring this question and the related question for the ring\nof integers of a number field.\n LOCATION:https://researchseminars.org/talk/Vinberg/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxim Kontsevich (IHES) DTSTART:20220223T153000Z DTEND:20220223T170000Z DTSTAMP:20260422T212936Z UID:Vinberg/10 DESCRIPTION:Title: Introduction to wall-crossing\nby Maxim Kontsevich (IHES) as part of The Vinberg Lecture Series\n\n\nAbstract\nWall-crossing structures appeare d several years ago in several mathematical contexts\, including cluster a lgebras and theory of generalized Donaldson-Thomas invariants. In my lectu re I will describe the general formalism based on a graded Lie algebra and an additive map from the grading lattice to an oriented plane ("central c harge").\n\nA geometric example of a wall-crossing structure comes from th eory of translation surfaces. The number of saddle connections in a given homology class is an integer-valued function on the parameter space (modul i space of abelian or quadratic differentials)\, which jumps along certain walls. The whole theory can be made totally explicit in this case. Also\, I'll talk about another closely related example\, which can be dubbed a " holomorphic Morse-Novikov theory".\n LOCATION:https://researchseminars.org/talk/Vinberg/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David Fisher (Indiana University) DTSTART:20220323T143000Z DTEND:20220323T160000Z DTSTAMP:20260422T212936Z UID:Vinberg/11 DESCRIPTION:Title: Arithmeticity\, superrigidity\, and totally geodesic submanifolds\nby David Fisher (Indiana University) as part of The Vinberg Lecture Series\n \n\nAbstract\nArithmeticity of locally symmetric spaces is an old and impo rtant\narea of study in which Vinberg proved some central results. I will \ndiscuss the history of the area\, some open questions and then\nfocus on recent joint work with Bader\, Miller and Stover. We prove\nthat non-ari thmetic real and complex hyperbolic manifolds cannot\nhave infinitely man y maximal totally geodesic submanifolds.\n LOCATION:https://researchseminars.org/talk/Vinberg/11/ END:VEVENT BEGIN:VEVENT SUMMARY:David Kazhdan (Hebrew University\, Israel) DTSTART:20220413T143000Z DTEND:20220413T160000Z DTSTAMP:20260422T212936Z UID:Vinberg/14 DESCRIPTION:Title: On the Langlands correspondence for curves over local fields\nby Davi d Kazhdan (Hebrew University\, Israel) as part of The Vinberg Lecture Seri es\n\n\nAbstract\nOn results and (mostly) conjectures on automorphic funct ions on moduli spaces of 2-dimensional vector bundles on curves over local fields.\n LOCATION:https://researchseminars.org/talk/Vinberg/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Pak (UCLA) DTSTART:20220504T163000Z DTEND:20220504T183000Z DTSTAMP:20260422T212936Z UID:Vinberg/16 DESCRIPTION:Title: Combinatorial inequalities\nby Igor Pak (UCLA) as part of The Vinberg Lecture Series\n\n\nAbstract\nIn the ocean of combinatorial inequalities\ , two islands are especially difficult. First\, Mason's conjectures say t hat the number of forests in a graph with k edges is log-concave. More ge nerally\, the number of independent sets of size k in a matroid is log-con cave. Versions of these results were established just recently\, in a rem arkable series of papers by Huh and others\, inspired by algebro-geometric considerations. \n\nSecond\, Stanley's inequality for the numbers of lin ear extensions of a poset with value k at a given poset element\, is log-c oncave. This was originally conjectured by Chung\, Fishburn and Graham\, and famously proved by Stanley in 1981 using the Alexandrov–Fenchel ineq ualities in convex geometry. No direct combinatorial proof for either res ult is known. Why not? \n\nIn the first part of the talk we will survey a number of combinatorial inequalities. We then present a new framework o f combinatorial atlas which allows one to give elementary proofs of the tw o results above\, and extend them in several directions. This talk is aim ed at the general audience.\n LOCATION:https://researchseminars.org/talk/Vinberg/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Kac (MIT) DTSTART:20230424T150000Z DTEND:20230424T170000Z DTSTAMP:20260422T212936Z UID:Vinberg/17 DESCRIPTION:Title: Exceptional de Rham complexes\nby Victor Kac (MIT) as part of The Vin berg Lecture Series\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Vinberg/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Borcherds (UC Berkeley) DTSTART:20240226T160000Z DTEND:20240226T180000Z DTSTAMP:20260422T212936Z UID:Vinberg/18 DESCRIPTION:Title: Vinberg’s Algorithm and Kac-Moody algebras\nby Richard Borcherds (U C Berkeley) as part of The Vinberg Lecture Series\n\n\nAbstract\nVinberg ’s algorithm was introduced by Vinberg in order to calculate the fundame ntal domains of hyperbolic reflection groups\, especially those coming fro m Lorentzian lattices. We will show how to use it to calculate the automor phism groups of some lattices\, culminating in Conway’s spectacular disc overy that the Dynkin diagram of the 26-dimensional even unimodular Lorent zian lattice is the Leech lattice. We will then discuss some of the Kac-Mo ody algebras associated with Vinberg’s Dynkin diagrams.\n LOCATION:https://researchseminars.org/talk/Vinberg/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Loseu (Yale University) DTSTART:20241213T170000Z DTEND:20241213T190000Z DTSTAMP:20260422T212936Z UID:Vinberg/19 DESCRIPTION:Title: Quantizations and unitary representations\nby Ivan Loseu (Yale Univer sity) as part of The Vinberg Lecture Series\n\n\nAbstract\nThe study of un itary representations of Lie groups is a classical subject in Representati on theory going back to Gelfand and Harish-Chandra. The main\, currently o pen\, problem is to classify the irreducible unitary representations of se misimple Lie groups. Thanks to the work of Kirillov and Kostant the questi on of classifying the irreducibles fits into Geometric quantization that s eeks to produce quantum mechanical systems from classical ones. In my talk I will explain some recent advances in Algebraic (a.k.a. Deformation) qua ntization of singular symplectic varieties and how they help to understand unipotent representations\, an important class of unitary representations that are expected to serve as building blocks. This is based on my solo w orks as well as joint papers with Dmytro Matvieievskyi\, Lucas Mason-Brown and Shilin Yu.\n LOCATION:https://researchseminars.org/talk/Vinberg/19/ END:VEVENT END:VCALENDAR