Eigenvarieties, families of Galois representations, p-adic L-functions

Prerequisite

Basic commutative algebra, algebraic geometry, algebraic number theory

Abstract

This course is intended to give a gentle introduction to p-adic families of modular forms and p-adic L-functions. We roughly cover the contents of "The Eigenbook" by Belliache. We will start by introducing a general construction of eigenvariety, and discuss modular symbols and their connection to modular forms. Then we will use the tools to construct and study the eigencurve and families of p-adic L-functions it carries.

Lecturer Intro.

Yong Suk Moon joined BIMSA in 2022 fall as an assistant research fellow. His research area is number theory and arithmetic geometry. More specifically, his current research focuses on p-adic Hodge theory, Fontaine-Mazur conjecture, and p-adic Langlands program. He completed his Ph.D at Harvard University in 2016, and was a Golomb visiting assistant professor at Purdue University (2016-19) and a postdoctoral researcher at University of Arizona (2019 - 22).