BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Katz (Ohio State) DTSTART:20210521T190000Z DTEND:20210521T200000Z DTSTAMP:20260407T214859Z UID:agstanford/50 DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Katz (Oh io State) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nHo w do you integrate a 1-form on an algebraic curve over the p-adic numbers? One can integrate locally\, but because the topology is totally disconnec ted\, it's not possible to perform analytic continuation. For good reducti on curves\, this question was answered by Coleman who introduced analytic continuation by Frobenius. For bad reduction curves\, there are two notion s of integration: a local theory that is easy to compute\; and a global si ngle-valued theory that is useful for number theoretic applications. We di scuss the relationship between these integration theories\, concentrating on the p-adic analogue of Chen's iterated integration which is important f or the non-Abelian Chabauty method. We explain how to use combinatorial id eas\, informed by tropical geometry and Hodge theory\, to compare the two integration theories and outline an explicit approach to computing these i ntegrals. This talk will start from the beginning of the story and require s no background besides some fluency in algebraic geometry and topology. T his is joint work with Daniel Litt.\n\nThe synchronous discussion for Eric Katz’s talk is taking place not in zoom-chat\, but at https://tinyurl.c om/2021-05-21-ek (and will be deleted after ~3-7 days).\n LOCATION:https://researchseminars.org/talk/agstanford/50/ END:VEVENT END:VCALENDAR