Speaker:Gaiada Grossi
Date: 10:30 24/11/2023
Title: Elliptic curves in p-adic towers: an introduction to Iwasawa theory 

Abstract: Classical periods naturally arise in the study of L-functions attached to motives. Deligne predicted that the (twisted) 
critical values of an L-function are algebraic once normalised by a certain period. Later, Coates and Perrin-Riou conjectured that, 
under some conditions, such critical values can be interpolated by a p-adic measure. The main conjectures of Iwasawa theory relate 
these p-adic measures to certain algebraic objects called Selmer groups. When the motive comes from an elliptic curve E, 
Selmer groups encode information about the Mordell-Weil rank of E in p-adic towers. In this talk I will give a gentle introduction to 
Iwasawa theory for elliptic curves and explain how it can be used to give new results about the Birch and Swinnerton-Dyer conjecture.