Exceptional isogenies between elliptic curves

Algebra Seminar
Monday, November 3, 2014 - 3:00pm
1 hour (actually 50 minutes)
Skiles 005
MIT and Paris-Sud
We will discuss a proof of the following result: if E and E' are two elliptic curves over a number field, there exist infinitely many places p of k such that the reduction of E and E' modulo p are isogenous. We will explain the relationship with the dynamics of Hecke correspondences on modular curves and the heuristics behind such results.