BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Brody Lynch (UMass Amherst)
DTSTART:20260217T210000Z
DTEND:20260217T220000Z
DTSTAMP:20260824T074904Z
UID:FCNTS/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/19/">E
 quidistribution of realizable Steinitz classes for Kummer extensions</a>\n
 by Brody Lynch (UMass Amherst) as part of Pioneer Valley Number Theory Sem
 inar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\nLet
  $\\ell$ be prime\, and $K$ be a number field containing the $\\ell$-th ro
 ots of unity. We use techniques from classical algebraic number theory to 
 prove that the Steinitz classes of $\\Z/\\ell\\Z$ extensions of $K$ are eq
 uidistributed among realizable classes in the ideal class group of $K$. Si
 milar equidistribution results have been proved for Galois groups $S_2$ an
 d $S_3$ by Kable and Wright and $S_4$ and $S_5$ by Bhargava\, Shankar\, an
 d Wang using the theory of prehomogeneous vector spaces\, but this is the 
 first complete equidistribution result for an infinite class of Galois gro
 ups.\n\nNext\, we discuss generalizations of this result to elementary-$\\
 ell$ Galois groups using $V_4$ as an example. Additionally\, we will give 
 some initial results for Steinitz classes of ray class fields.\n
LOCATION:https://researchseminars.org/talk/FCNTS/19/
END:VEVENT
END:VCALENDAR