BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lillian Pierce DTSTART:20210602T150000Z DTEND:20210602T160000Z DTSTAMP:20260418T064636Z UID:LNTS/40 DESCRIPTION:Title: Co unting problems\, from the perspective of moments\nby Lillian Pierce a s part of London number theory seminar\n\n\nAbstract\nMany questions in nu mber theory can be phrased as counting problems. How many number fields ar e there? How many elliptic curves are there? How many integral solutions t o this system of Diophantine equations are there? If the answer is “infi nitely many\,” we want to understand the order of growth for the number of objects we are counting in the “family." But in many settings we are also interested in finer-grained questions\, like: how many number fields are there\, with fixed degree and fixed discriminant? We know the answer i s “finitely many\,” but it would have important consequences if we cou ld show the answer is always “very few indeed.” In this talk\, we will describe a way that these finer-grained questions can be related to the b igger infinite-family questions. Then we will use this perspective to surv ey interconnections between several big open conjectures in number theory\ , related in particular to class groups and number fields.\n LOCATION:https://researchseminars.org/talk/LNTS/40/ END:VEVENT END:VCALENDAR