BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Prof. Samit Dasgupta & Prof. Mahesh Kakde (Duke University & India n Institute of Science\, respectively) DTSTART:20220209T123000Z DTEND:20220209T140000Z DTSTAMP:20260423T005648Z UID:tmc-dls/26 DESCRIPTION:Title: On Brumer-Stark units and Hilbert's 12th problem\nby Prof. Samit Dasg upta & Prof. Mahesh Kakde (Duke University & Indian Institute of Science\, respectively) as part of TMC Distinguished Lecture Series\n\n\nAbstract\n Class field theory describes abelian extensions of a number field in terms of data intrinsic to the field. Hilbert’s 12th problem\, or explicit cl ass field theory\, goes further and asks for explicit generators of abelia n extensions of a number field as values of analytic functions. Stark’s conjectures provide a different perspective by postulating existence of sp ecial elements\, now called Stark units\, related to leading terms of L-fu nctions at s=0 and generating abelian extensions of a number field. In thi s talk we will first review classical results on explicit class field theo ry for the field of rational numbers and imaginary quadratic fields. Next we review Stickelberger’s theorem on annihilation of class groups of abe lian extensions of the field of rational numbers. Brumer-Stark conjecture is an analogue of Stickelberger’s theorem for arbitrary totally real fie lds. We will see the statement of this conjecture along with its refinemen ts and our results towards them. We prove these conjectures away from p=2 Brumer-Stark conjecture gives existence of special elements called Brumer -Stark units. These generate abelian extensions of a totally real number f ield. A conjecture by one of us gives p-adic analytic formulae for Brumer- Stark units. We will discuss this conjecture. Our recent work proves this conjecture away from p=2 thus providing a p-adic analytic solution to Hilb ert’s 12th problem for totally real number fields. We will end with a br ief sketch of our proofs.\n LOCATION:https://researchseminars.org/talk/tmc-dls/26/ END:VEVENT END:VCALENDAR