BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yotam Hendel (Northwestern) DTSTART:20200617T133000Z DTEND:20200617T143000Z DTSTAMP:20260423T041354Z 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 END:VCALENDAR