BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ashvin Swaminathan (Harvard) DTSTART:20221011T203000Z DTEND:20221011T213000Z DTSTAMP:20260423T130410Z UID:MITNT/57 DESCRIPTION:Title: G eometry-of-numbers in the cusp\, and class groups of orders in number fiel ds\nby Ashvin Swaminathan (Harvard) as part of MIT number theory semin ar\n\nLecture held in Room 2-143 in the Simons Building (building 2).\n\nA bstract\nIn this talk\, we discuss the distributions of class groups of or ders in number fields. We explain how studying such distributions is relat ed to counting integral orbits having bounded invariants that lie inside t he cusps of fundamental domains for coregular representations. We introduc e two new methods to solve this counting problem\, and as an example\, we demonstrate how one of these methods can be used to determine the average size of the 2-torsion in the class groups of totally real or complex cubic orders\, when such orders are enumerated by discriminant. Much of this wo rk is joint with Arul Shankar\, Artane Siad\, and Ila Varma.\n LOCATION:https://researchseminars.org/talk/MITNT/57/ END:VEVENT END:VCALENDAR