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DTSTAMP:20260910T163449Z
DESCRIPTION:Title: Stark's Conjectures and Hilbert's 12th Problem.\n\nAbstr
 act: In this talk we will discuss two central problems in algebraic number
  theory and their interconnections: explicit class field theory and the sp
 ecial values of L-functions.  The goal of explicit class field theory is t
 o describe the abelian extensions of a ground number field via analytic me
 ans intrinsic to the ground field\; this question lies at the core of Hilb
 ert's 12th Problem.  Meanwhile\, there is an abundance of conjectures on t
 he values of L-functions at certain special points.  Of these\, Stark's Co
 njecture has relevance toward explicit class field theory.  I will describ
 e two recent joint results with Mahesh Kakde on these topics.  The first i
 s a proof of the Brumer-Stark conjecture away from p=2. This conjecture st
 ates the existence of certain canonical elements in abelian extensions of 
 totally real fields.  The second is a proof of an exact formula for Brumer
 -Stark units that has been developed over the last 15 years.  We show that
  these units together with other easily written explicit elements generate
  the maximal abelian extension of a totally real field\, thereby giving a 
 p-adic solution to the question of explicit class field theory for these f
 ields.\n\n \n\n \n\nColloque des sciences mathématiques du Québec\n	Hybride
  -Places limitées- Salle 5340\, pavillon André-Aisenstadt /Zoom: https://u
 montreal.zoom.us/j/93983313215?pwd=clB6cUNsSjAvRmFMME1PblhkTUts... ID de r
 éunion : 939 8331 3215 Code secret : 096952\n
DTSTART:20211210T190000Z
DTEND:20211210T200000Z
SUMMARY:Samit Dasgupta (Duke University)
URL:https://www.mcgill.ca/mathstat/channels/event/samit-dasgupta-duke-unive
 rsity-335390
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