Speaker: Andrei Jorza (Notre Dame)

Title: p-adic interpolations and L-functions

Abstract: The classical Birch and Swinnerton-Dyer conjecture (one of the million dollar Millenium Problems) posits a relationship between the arithmetic and complex analytic behaviors of elliptic curves. Recent progress towards this conjecture relies on the p-adic analytic behavior of these elliptic curves, which can be thought of as an intermediary between arithmetic and complex analysis. I will describe what it means to p-adically interpolate complex analytic L-functions and some p-adic analogues of the Birch and Swinnerton-Dyer conjecture.