BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Katz (Ohio State University) DTSTART:20211105T140000Z DTEND:20211105T150000Z DTSTAMP:20260423T035456Z UID:LAGARTOS/32 DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Katz (Ohio State University) as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nHow do you integrate a 1-form on an algebr aic curve over the p-adic numbers? One can integrate locally\, but because the topology is totally disconnected\, it's not possible to perform analy tic continuation. For good reduction curves\, this question was answered b y Coleman who introduced analytic continuation by Frobenius. For bad reduc tion curves\, there are two notions of integration: a local theory that is easy to compute\; and a global single-valued theory that is useful for nu mber theoretic applications. We discuss the relationship between these int egration theories\, concentrating on the p-adic analogue of Chen's iterate d integration which is important for the non-Abelian Chabauty method. We e xplain how to use combinatorial ideas\, informed by tropical geometry and Hodge theory\, to compare the two integration theories and outline an expl icit approach to computing these integrals. This is joint work with Daniel Litt.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/32/ END:VEVENT END:VCALENDAR