BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Iordan Ganev (WIS) DTSTART:20200527T133000Z DTEND:20200527T143000Z DTSTAMP:20260404T094801Z UID:AlgWies/1 DESCRIPTION:Title: Beilinson-Bernstein localization via wonderfulasymptotics.\nby Iordan Ganev (WIS) as part of Seminar on Representation Theory and Algebra ic Geometry\n\n\nAbstract\nWe explain how a doubled version of theBeilinso n-Bernstein localization functor can be understood using the geometryof th e wonderful compactification of a group. Specifically\, bimodules for theL ie algebra give rise to monodromic D-modules on the horocycle space\, and tofiltered D-modules on the group that respect a certain matrix coefficien tsfiltration. These two categories of D-modules are related via an associa tedgraded construction in a way compatible with localization\, Verdier spe cialization\,the Vinberg semigroup\, and additional structures. This talk is based on jointwork with David Ben-Zvi.\n LOCATION:https://stable.researchseminars.org/talk/AlgWies/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Shachar Carmeli (WIS) DTSTART:20200603T133000Z DTEND:20200603T143000Z DTSTAMP:20260404T094801Z UID:AlgWies/2 DESCRIPTION:Title: A relative de Rham theorem for Nash Submersions\nby Shachar Car meli (WIS) as part of Seminar on Representation Theory and Algebraic Geome try\n\n\nAbstract\nFor a Nash manifold X and a Nash vector bundle E on X\, one can form the topological vector space of Schwartz sections of E\, i.e . the smooth sections which decay fast along with all derivatives. It was shown by Aizenbud and Gourevitch\, and independently by Luca Prelli\, tha t for a Nash manifold X\, th complex of Schwartz sections of the de Rham c omplex of X has cohomologies isomorphic to the compactly supported cohomol ogies of X. \n \nIn my talk I will present a work in progress\, joint with Avraham Aizenbud\, to generalize this result to the relative case\, repla cing the Nash manifold M with a Nash submersion f:M-->N. Using infinity ca tegorical methods\, I will define the notion of a Schwartz section of a Na sh bundle E over a complex of sheaves with constructible cohomologies\, ge neralizing the notion of Schwartz section on an open semialgebraic set. I will then relate the Schwartz sections of the relative de Rham complex of a Nash submersion f:M-->N with the Schwartz functions on N over the derive d push-forward with proper support of the constant sheaf on M. Finally\, I will coclude with some applications to the relation between the Schwartz sections of the relative de Rham complex and the topology of the fibers of f\n LOCATION:https://stable.researchseminars.org/talk/AlgWies/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Miller (Rutgers) DTSTART:20200610T133000Z DTEND:20200610T143000Z DTSTAMP:20260404T094801Z UID:AlgWies/3 DESCRIPTION:Title: TBA\nby Steve Miller (Rutgers) as part of Seminar on Representa tion Theory and Algebraic Geometry\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/AlgWies/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yotam Hendel (Northwestern) DTSTART:20200617T133000Z DTEND:20200617T143000Z DTSTAMP:20260404T094801Z UID:AlgWies/4 DESCRIPTION:Title: Singularity properties of convolutions of algebraicmorphisms and pr obabilistic Waring type problems Abstract:\nby Yotam Hendel (Northwest ern) as part of Seminar on Representation Theory and Algebraic Geometry\n\ n\nAbstract\nLet G be a connected algebraic group. \nWe define and study a convolution operation between algebraic morphisms intoG. We show that t his operation yields morphisms with improved singularityproperties\, and i n particular\, that under reasonable assumptions one can alwaysobtain a fl at morphism with reduced fibers of rational singularities (termed anFRS mo rphism) after enough convolutions.\nThe FRS property is of high importance since (FRS) morphisms can becharacterized by good asymptotic behaviour of the number of points of theirfibers over finite rings of the form Z/p^kZ. \nThis further allows us to interpret the FRS property through probabilis ticlenses.\nWe discuss some of the above\, motivated by the special case o f word maps whichcan be viewed as a relative \nanalogue in the settings of p-adic groups of Waring's problem from 1770 (seearXiv:1912.12556).\nJoint work with Itay Glazer.\n LOCATION:https://stable.researchseminars.org/talk/AlgWies/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gal Dor (TAU) DTSTART:20200605T133000Z DTEND:20200605T143000Z DTSTAMP:20260404T094801Z UID:AlgWies/5 DESCRIPTION:Title: Algebraic structures on automorphic L-functions\nby Gal Dor (TA U) as part of Seminar on Representation Theory and Algebraic Geometry\n\n\ nAbstract\nConsiderthe function field $F$ of a smooth curve over $\\mathbb {F}_q$\, with $q\\neq 2$.\n\nL-functions of automorphic representations of $\\GL(2)$over $F$ are important objects for studying the arithmetic prope rties of thefield $F$. Unfortunately\, they can be defined in two differen t ways: one byGodement-Jacquet\, and one by Jacquet-Langlands. Classically \, one shows that theresulting L-functions coincide using a complicated co mputation.\n\n \n\nI will present a conceptual proof that the two families coincide\, by categorifying the question. This correspondence will necessi tatecomparing two very different sets of data\, which will have significan timplications for the representation theory of $\\GL(2)$. In particular\, we willobtain an exotic symmetric monoidal structure on the category ofrep resentations of $\\GL(2)$\n LOCATION:https://stable.researchseminars.org/talk/AlgWies/5/ END:VEVENT END:VCALENDAR