BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ray Li (University of Chicago) DTSTART:20260916T200000Z DTEND:20260916T205000Z DTSTAMP:20261004T235438Z UID:UtahRTNT/22 DESCRIPTION:Title: Overconvergent deformation theory\nby Ray Li (University of Chicago) as part of University of Utah Representation Theory / Number Theory Semin ar\n\nLecture held in LCB 222.\n\nAbstract\nIn the study of moduli spaces a useful starting point is to understand their local structure\, i.e.\, th eir versal rings. For example\, for the Emerton--Gee stack this gives the Galois deformation rings. For a p-adic analytic stack these should be over convergent rings or analytic germs\; these are not limits of Artinian ring s hence require different tools to study. I will describe a theory for con structing and studying analytic versal rings using a Koszul duality in a $ p$-adic analytic setting.\nIn spirit it is perhaps closest to the complex analytic deformation theory of Kuranishi and Kodaira--Nirenberg--Spencer t hough (a light amount of) light solid mathematics plays an important found ational role.\n\nI will mention two applications: one to the analytic Emer ton--Gee stack and one to the relativistic $p$-adic sunscreen conjecture o f Sean Howe on intersections of analytic manifolds with Banach--Colmez spa ces.\n LOCATION:https://researchseminars.org/talk/UtahRTNT/22/ END:VEVENT END:VCALENDAR