## Columbia Mathematics Department
Colloquium

*Expliciting** the local Langlands correspondence*

### by

### Guy Henniart

### University of
Paris-Sud

Abstract:

All
elliptic curves over Q are now known to be modular, and this implies Fermat's
Last theorem.

Those
results belong to the framework of the Langlands
program, which conjectures precise links

between Galois
representations and modular forms (for GL(2)), or more generally automorphic

forms for
reductive groups G. There is a local counterpart, presumably easier,
and actually proved,

over the field Q_p of p-adic numbers, relating
Galois representations of degree n with
linear

(infinite
dimensional usually) representations of GL(n, Q_p). Both sides, when n is prime to p for

example, have a very reasonable explicit
description. But describing the Langlands
correspondence

explicitly is a
nightmare. Please come and share!

**Nov. 17th, Wednesday, 5:00-6:00 pm**

**Mathematics
520**

**Tea will be
served at 4:30pm**