Events

Samit Dasgupta

Duke University
Colloquia

When

Date: Wednesday, November 9, 2022
Time: 3:30 pm - 5:00 pm
Location: Petty 150
Dr Samit Dasgupta is a professor at Duke University He received a Ph D degree in 2004 from University of California, Berkeley, and a bachelor's degree in 1999 from Harvard University Professor Dasgupta received a Sloan Research Fellowship in 2009 and an NSF CAREER award in 2010 His research is in algebraic number theory, specifically the explicit construction of units in number fields and points on abelian varieties Much of his work uses the theory of modular forms and their associated Galois representations in order to shed light on these problems Professor Dasgupta was named a fellow of the American Mathematical Society, in the 2022 class of fellows,fellows,"for contributions to number theory, in particular the theory of special values of classical and p adic L functions"

In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory and the special values of L-functions.  The goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field; this question lies at the core of Hilbert’s 12th Problem.  I will describe two recent joint results with Mahesh Kakde on these topics.  The first is a proof of the Brumer-Stark conjecture. This conjecture states the existence of certain canonical elements in CM 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 fields.