Mathematics Colloquium: Francesc Castella, Iwasawa theory and the arithmetic of elliptic curves
This event is in the past.
When:
December 11, 2023
2:45 p.m. to 3:45 p.m.
2:45 p.m. to 3:45 p.m.
Where:
Event category:
Seminar
In-person
Colloquium: Iwasawa theory and the arithmetic of elliptic curves.
Speaker: Francesc Castella (UC Santa Barbara)
Abstract: Iwasawa theory is a fundamental tool for the study of the mysterious links between arithmetic objects (such as class groups of number fields and rational points on abelian varieties) and special values of L-functions, as predicted by conjectures in the spirit of Birch and Swinnerton-Dyer. A key idea is to deform the given algebraic and analytic objects into naturally occurring p-adic families, and to deduce "by descent" information from the much-better behaved avatars one obtains in the limit. In this talk, I will illustrate some of these ideas in the contexts of classical Iwasawa theory and the arithmetic of elliptic curves, including some recent applications of these methods.