BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Distributions of unramified extensions of global fields - Melanie 
 Matchett Wood (Harvard)
DTSTART:20230510T133000Z
DTEND:20230510T143000Z
UID:TALK200233@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Every number field K has a maximal unramified extension Kun\, 
 with\nGalois group Gal(Kun/K) (whose abelianization is the class group of\
 nK).  As K varies\, we ask about the distribution of the groups\nGal(Kun/K
 ).  We give a conjecture about this distribution\, which we\nalso conjectu
 re in the function field analog.  We give some results\nabout Gal(Kun/K) t
 hat motivate us to build certain random groups\nwhose distributions appear
  in our conjectures.  We give theorems in\nthe function field case (as the
  size of the finite field goes to\ninfinity) that support these new conjec
 tures.  In particular\, our\ndistributions abelianize to the Cohen-Lenstra
 -Martinet distributions\nfor class groups\, and so our function field theo
 rems give support to\n(suitably modified) versions of the Cohen-Lenstra-Ma
 rtinet heuristics.\nThis talk is on joint work with Yuan Liu and David Zur
 eick-Brown\, and\nwith Will Sawin.\n
LOCATION:MR15
END:VEVENT
END:VCALENDAR