Sophie Morel

(Princeton University)

March 10, 9-11 and 12:30-14:00

**Cohomology of Shimura varieties**

(morning)

I will explain the conjectural

description of the cohomology of a Shimura variety and how people have

tried to prove this conjecture, on the example of a Siegel modular 3-fold.

If time permits, I’ll also talk about the applications to the Langlands

program for GL_n.

**R=T theorems**

(afternoon)

I will explain what R and T stand for

(ie universal deformation ring of Galois representations and ring of Hecke

operators acting on a space of modular/automorphic forms), how to

reformulate the Langlands correspondence as a R=T theorem, and why Vincent

Lafforgue’s can be interpreted as the construction of a surjective map

R->T.

Place: IPM, Niavaran Building