BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Melanie Matchett Wood (Harvard) DTSTART:20220426T203000Z DTEND:20220426T213000Z DTSTAMP:20260423T124855Z UID:MITNT/49 DESCRIPTION:Title: D istributions of unramified extensions of global fields\nby Melanie Mat chett Wood (Harvard) as part of MIT number theory seminar\n\nLecture held in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nEvery numb er field K has a maximal unramified extension K^un\, with\nGalois group Ga l(K^un/K) (whose abelianization is the class group of\nK).  As K varies\, we ask about the distribution of the groups\nGal(K^un/K).  We prove some results about the structure of Gal(K^un/K) \nthat motivate us to give a c onjecture about this distribution\, which we\nalso conjecture in the funct ion field analog.  We give theorems in\nthe function field case (as the s ize of the finite field goes to\ninfinity) that support these new conjectu res.  In particular\, our\ndistributions abelianize to the Cohen-Lenstra- Martinet distributions\nfor class groups\, and so our function field theor ems prove\n(suitably modified) versions of the Cohen-Lenstra-Martinet heur istics\nover function fields as the size of the finite field goes to\ninfi nity.  This talk is on joint work with Yuan Liu and David Zureick-Brown.\ n LOCATION:https://researchseminars.org/talk/MITNT/49/ END:VEVENT END:VCALENDAR