This is a series of three lectures: 11:00 AM - 12:00 PM on May 24, May 31, and June 7.
Zoom Meeting ID: 830 9045 0287
Talk 1: Iwasawa Theory: Background The first talk will be introductory in nature and the aim will be to make sure that non-experts can follow the remaining of the lecture series. We will start by discussing the notions introduced by Iwasawa starting in the late 1950's. We will then describe the work of Mazur (from 1972) which started the subject of "Iwasawa theory of Selmer groups of elliptic curves". We will briefly explain the contributions of Greenberg, some of which we will return to in the subsequent lectures.
Talk 2: Iwasawa Theory of Fine Selmer Groups of elliptic curves We will start by introducing the notion of fine Selmer group of an elliptic curve, the study of which was initiated by Coates-Sujatha (2005). As we will see, these objects are subgroups of Selmer groups which are very closely related to class groups. Motivated by conjectures in classical Iwasawa theory, they formulated two conjectures for fine Selmer groups of elliptic curves. I will report on some modest progress I made in this direction during my PhD.
Talk 3: Statistics for Iwasawa Invariants In my final talk, I will discuss some recent results (joint with Anwesh Ray). Here, we study the average behaviour of the Iwasawa invariants for the Selmer groups of elliptic curves, setting out new directions in arithmetic statistics and Iwasawa theory.