BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Betts (Cornell University) DTSTART:20260529T200000Z DTEND:20260529T210000Z DTSTAMP:20260603T012928Z UID:NTBU/51 DESCRIPTION:Title: To rsors over abelian varieties and quadratic Chabauty\nby Alex Betts (Co rnell University) as part of Boston University Number Theory Seminar\n\nLe cture held in CDS Room 548 in Boston University.\n\nAbstract\nThis talk co ncerns two generalisations of the Chabauty method\, which studies the rati onal points on a curve X by embedding it inside its Jacobian. The first is Kim's non-abelian Chabauty programme\, which replaces the Jacobian with a sequence of "Selmer schemes" produced from the fundamental group of X. Th e second is the geometric quadratic Chabauty method of Edixhoven and Lido\ , which replaces the Jacobian instead by a Gm-torsor over the Jacobian. Th ese two generalisations are related by work of Hashimoto\, Duque Rosero an d Spelier.\n\nThe main aim of this talk is to explain why these two approa ches are related\, with the punchline being that torsors under tori over a belian varieties have fundamental groups which exactly realise the quotien ts of pi_1(X) studied in the quadratic part of Chabauty—Kim. Time permit ting\, we will also explain how this perspective connects quadratic Chabau ty with a new kind of unlikely intersections problem\, and what this tells us about the structure of the quadratic Chabauty locus.\n LOCATION:https://researchseminars.org/talk/NTBU/51/ END:VEVENT END:VCALENDAR