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:20260422T212901Z UID:AlgWies/1 DESCRIPTION:Title: Beilinson-Bernstein localization via wonderfulasymptotics.\nby Iordan Ganev (WIS) as part of Seminar on Representation Theory and Algebraic Geom etry\n\n\nAbstract\nWe explain how a doubled version of theBeilinson-Berns tein localization functor can be understood using the geometryof the wonde rful compactification of a group. Specifically\, bimodules for theLie alge bra give rise to monodromic D-modules on the horocycle space\, and tofilte red D-modules on the group that respect a certain matrix coefficientsfiltr ation. These two categories of D-modules are related via an associatedgrad ed construction in a way compatible with localization\, Verdier specializa tion\,the Vinberg semigroup\, and additional structures. This talk is base d on jointwork with David Ben-Zvi.\n LOCATION:https://researchseminars.org/talk/AlgWies/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Shachar Carmeli (WIS) DTSTART:20200603T133000Z DTEND:20200603T143000Z DTSTAMP:20260422T212901Z UID:AlgWies/2 DESCRIPTION:Title: A relative de Rham theorem for Nash Submersions\nby Shachar Carmeli (W IS) as part of Seminar on Representation Theory and Algebraic Geometry\n\n \nAbstract\nFor a Nash manifold X and a Nash vector bundle E on X\, one ca n form the topological vector space of Schwartz sections of E\, i.e. the s mooth sections which decay fast along with all derivatives. It was shown by Aizenbud and Gourevitch\, and independently by Luca Prelli\, that for a Nash manifold X\, th complex of Schwartz sections of the de Rham complex of X has cohomologies isomorphic to the compactly supported cohomologies o f X. \n \nIn my talk I will present a work in progress\, joint with Avraha m Aizenbud\, to generalize this result to the relative case\, replacing th e Nash manifold M with a Nash submersion f:M-->N. Using infinity categoric al methods\, I will define the notion of a Schwartz section of a Nash bund le E over a complex of sheaves with constructible cohomologies\, generaliz ing the notion of Schwartz section on an open semialgebraic set. I will th en 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 derived push- forward with proper support of the constant sheaf on M. Finally\, I will c oclude with some applications to the relation between the Schwartz section s of the relative de Rham complex and the topology of the fibers of f\n LOCATION:https://researchseminars.org/talk/AlgWies/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Miller (Rutgers) DTSTART:20200610T133000Z DTEND:20200610T143000Z DTSTAMP:20260422T212901Z UID:AlgWies/3 DESCRIPTION:Title: TBA\nby Steve Miller (Rutgers) as part of Seminar on Representation Th eory and Algebraic Geometry\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/AlgWies/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yotam Hendel (Northwestern) DTSTART:20200617T133000Z DTEND:20200617T143000Z DTSTAMP:20260422T212901Z UID:AlgWies/4 DESCRIPTION:Title: Singularity properties of convolutions of algebraicmorphisms and probabili stic Waring type problems Abstract:\nby Yotam Hendel (Northwestern) as part of Seminar on Representation Theory and Algebraic Geometry\n\n\nAbst ract\nLet G be a connected algebraic group. \nWe define and study a convo lution operation between algebraic morphisms intoG. We show that this ope ration yields morphisms with improved singularityproperties\, and in parti cular\, that under reasonable assumptions one can alwaysobtain a flat morp hism with reduced fibers of rational singularities (termed anFRS morphism) after enough convolutions.\nThe FRS property is of high importance since (FRS) morphisms can becharacterized by good asymptotic behaviour of the nu mber of points of theirfibers over finite rings of the form Z/p^kZ. \nThis further allows us to interpret the FRS property through probabilisticlens es.\nWe discuss some of the above\, motivated by the special case of 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 w ith Itay Glazer.\n LOCATION:https://researchseminars.org/talk/AlgWies/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gal Dor (TAU) DTSTART:20200605T133000Z DTEND:20200605T143000Z DTSTAMP:20260422T212901Z UID:AlgWies/5 DESCRIPTION:Title: Algebraic structures on automorphic L-functions\nby Gal Dor (TAU) as p art of Seminar on Representation Theory and Algebraic Geometry\n\n\nAbstra ct\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 properties o f thefield $F$. Unfortunately\, they can be defined in two different ways: one byGodement-Jacquet\, and one by Jacquet-Langlands. Classically\, one shows that theresulting L-functions coincide using a complicated computati on.\n\n \n\nI will present a conceptual proof that the two familiescoincid e\, by categorifying the question. This correspondence will necessitatecom paring two very different sets of data\, which will have significantimplic ations for the representation theory of $\\GL(2)$. In particular\, we will obtain an exotic symmetric monoidal structure on the category ofrepresenta tions of $\\GL(2)$\n LOCATION:https://researchseminars.org/talk/AlgWies/5/ END:VEVENT END:VCALENDAR