Back to Departmental Colloquium: Fall 2024
Departmental Colloquium
Date: Thursday, Dec 5, 2024
Time: 4:00PM - 5:00PM
Location: JWB 335
Chandrashekhar Khare
UCLA
Title |
Modularity of Galois representations: from Ramanujan to Wiles |
Abstract |
I will give a historically motivated account of the connection between modular forms and Galois theory. Ramanujan’s 1916 paper “On some arithmetical functions” led to a series of developments that led to the proof of Fermat’s Last Theorem: one can draw a line from Ramanujan’s paper, to the formulation of Serre’s conjecture in the 1970’s and 1980’s, its connection to Fermat’s Last Theorem, and Wiles’s proof of Fermat in 1994. I will also indicate recent developments in the subject linking modular forms and Galois representations, for instance the proof of modularity of elliptic curves over Q(i) by Ana Cariani and James Newton, which relies on particular cases of an analog of Serre’s conjecture over Q(i) proved in joint work with Patrick Allen and Jack Thorne. |
Representation Theory
Number Theory
Distinguished Lecture Series