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SUMMARY:Arul Shankar (University of Toronto)
DTSTART:20201209T160000Z
DTEND:20201209T170000Z
DTSTAMP:20260423T024745Z
UID:hnts/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/17/">Th
 e number of $D_4$-extensions of $\\mathbb{Q}$</a>\nby Arul Shankar (Univer
 sity of Toronto) as part of Heilbronn number theory seminar\n\n\nAbstract\
 nWe will begin with a summary of how Malle's conjecture and Bhargava's heu
 ristics can be used to develop the "Malle--Bhargava heuristics"\, predicti
 ng the asymptotics in families of number fields\, ordered by a general cla
 ss of invariants.\n\nWe will then specialize in the case of $D_4$-number f
 ields. Even in this (fairly simple) case\, where the fields can be paramet
 rized quite explicitly\, the question of determining asymptotics can get q
 uite complicated. We will discuss joint work with Altug\, Varma\, and Wils
 on\, in which we recover asymptotics when quartic $D_4$ fields are ordered
  by conductor. And we will finally discuss joint work with Varma\, in whic
 h we recover Malle's conjecture for octic $D_4$-fields.\n
LOCATION:https://researchseminars.org/talk/hnts/17/
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