2017
Feb
27

# NT&AG: Eyal Goren (McGill University), "p-adic dynamics of Hecke operators"

3:00pm to 4:00pm

## Location:

Ross 70A

Abstract:

Motivated by understanding the action of Hecke operators on special sub-varieties of Shimura varieties, we consider the simplest possible case: the action of Hecke operators on the j-line, namely on the moduli space of elliptic curves, and in particular the action on singular moduli. Our interest is in this action considered in the p-adic topology. The emerging picture is surprisingly rich and the answers involve Serre-Tate coordinates, the Gross-Hopkins period map and finally involves random walks on GL_n.

This is joint work with Payman Kassaei (King's College).

Motivated by understanding the action of Hecke operators on special sub-varieties of Shimura varieties, we consider the simplest possible case: the action of Hecke operators on the j-line, namely on the moduli space of elliptic curves, and in particular the action on singular moduli. Our interest is in this action considered in the p-adic topology. The emerging picture is surprisingly rich and the answers involve Serre-Tate coordinates, the Gross-Hopkins period map and finally involves random walks on GL_n.

This is joint work with Payman Kassaei (King's College).