BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lars Kühne (University of Copenhagen) DTSTART:20210621T111500Z DTEND:20210621T121500Z DTSTAMP:20260423T041509Z UID:WarsawNT/36 DESCRIPTION:Title: Equidistribution and Uniformity in Families of Curves\nby Lars Kühn e (University of Copenhagen) as part of Warsaw Number Theory Seminar\n\nLe cture held in currently online.\n\nAbstract\nIn the talk\, I will present an equidistribution result for fa milies of (non-degenerate) subvarieties in a (general) family of abelian varieties. This extends a result of DeMar co and Mavraki for curves in fibered products of elliptic surfaces. Using this result\, one can deduce a uniform version of the classical Bogomolov conjecture for curves embed ded in their Jacobians\, namely that the numbe r of torsion points lying on them is uniformly bounded in the genus of the curve. This has been previously only known in a few select cases by work of David–Philippon and DeMarco–Krieger–Ye. Finally\, one can obtain a rather uniform version of the Mordell-Lang conjecture as well by complem enting a re sult of Dimitrov–Gao–Habegger: The number of rational poin ts on a smooth algebraic curve defined over a number field can be bounded solely in terms of its genus and the Mordell-Weil rank of its Jacobian. Ag ain\, this was previously known only under additional assumptions (Stoll\, Katz–Rabinoff–Zureick-Brown).\n LOCATION:https://researchseminars.org/talk/WarsawNT/36/ END:VEVENT END:VCALENDAR