BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nirvana Coppola (Vrije Universiteit Amsterdam) DTSTART:20220223T160000Z DTEND:20220223T170000Z DTSTAMP:20260418T065333Z UID:LNTS/62 DESCRIPTION:Title: Co leman integrals over number fields: a computational approach\nby Nirva na Coppola (Vrije Universiteit Amsterdam) as part of London number theory seminar\n\n\nAbstract\nOne of the deepest mathematical results is Faltings 's Theorem on the finiteness of rational points on an algebraic curve of g enus $g \\geq 2$. A much more difficult question\, still not completely an swered\, is whether given a curve of genus $g \\geq 2$\, we can find all i ts rational points\, or\, more in general\, all points defined over a cert ain number field. An entire (currently very active!) area of research is d evoted to find an answer to such questions\, using the "method of Chabauty ".\n\nIn this seminar\, I will talk about one of the first tools employed in Chabauty method\, namely Coleman integrals\, which Coleman used to comp ute an explicit bound on the number of rational points on a curve. After e xplaining how this is defined\, I will give a generalisation of this defin ition for curves defined over number fields\, and explain how to explicitl y compute these integrals. This is based on an ongoing project\, which sta rted during the Arizona Winter School 2020\, joint with E. Kaya\, T. Kelle r\, N. Müller\, S. Muselli.\n LOCATION:https://researchseminars.org/talk/LNTS/62/ END:VEVENT END:VCALENDAR