BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:John Voight (John Voight) DTSTART:20200620T190000Z DTEND:20200620T195000Z DTSTAMP:20260415T002709Z UID:CNTD2020/3 DESCRIPTION:Title: Archimedean aspects of the Cohen-Lenstra heuristics\nby John Voight ( John Voight) as part of Chicago Number Theory Day 2020\n\n\nAbstract\nLike rational points on elliptic curves\, units in number rings are gems of ar ithmetic. Refined questions about units remain difficult to answer\, ofte n embedded within difficult questions about class groups. For example: ho w often in a number ring is it that all totally positive units are squares ? \n\nAbsent theorems\, we may still try to predict the answer to these qu estions. In this talk\, we present heuristics (and some theorems!) for si gnatures of unit groups\, inspired by the Cohen-Lenstra heuristics\, formu lating precise conjectures and providing evidence for them. A key role is played by a lustrous structure of number rings we call the 2-Selmer signa ture map. This structure clarifies the provenance of reflection theorems\ , like those due to Leopoldt\, Armitage-Frohlich\, and Gras. \n\nThis is j oint work with David S. Dummit and Richard Foote and with Ben Breen\, Noam Elkies\, and Ila Varma.\n LOCATION:https://researchseminars.org/talk/CNTD2020/3/ END:VEVENT END:VCALENDAR