Title: On the modularity of elliptic curves over imaginary quadratic fields

Date: 11/20/2019

Time: 3:00 PM - 4:00 PM

Place: C304 Wells Hall

The Langlands-Tunnell theorem is an important starting point in Wiles's proof of the modularity of semistable elliptic curves over the rationals. Over imaginary quadratic fields it is unclear how to similarly use the Langlands-Tunnell theorem and Wiles's strategy runs into problems right from the start. I will motivate and explain the subtle but fundamental issues that arise, and indicate how they can be circumvented in many cases. As an application, we deduce that a positive proportion of elliptic curves over imaginary quadratic fields are modular. This is joint work with Chandrashekhar Khare and Jack Thorne.