BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Litt (University of Georgia) DTSTART:20210430T220000Z DTEND:20210430T230000Z DTSTAMP:20260423T040107Z UID:UCSBsga/21 DESCRIPTION:Title: The tropical section conjecture\nby Daniel Litt (University of Georgi a) as part of UCSB Seminar on Geometry and Arithmetic\n\n\nAbstract\nGroth endieck's section conjecture predicts that for a curve X of genus at least 2 over an arithmetically interesting field (say\, a number field or p-adi c field)\, the étale fundamental group of X encodes all the information a bout rational points on X. In this talk I will formulate a tropical analog ue of the section conjecture and explain how to use methods from low-dimen sional topology and moduli theory to prove many cases of it. As a byproduc t\, I'll construct many examples of curves for which the section conjectur e is true\, in interesting ways. For example\, I will explain how to prove the section conjecture for the generic curve\, and for the generic curve with a rational divisor class\, as well as how to construct curves over p- adic fields which satisfy the section conjecture for geometric reasons. Th is is joint work with Wanlin Li\, Nick Salter\, and Padma Srinivasan.\n LOCATION:https://researchseminars.org/talk/UCSBsga/21/ END:VEVENT END:VCALENDAR