## Columbia Mathematics Department
Colloquium

*Kloosterman** sheaves for
reductive groups *

### by

### Ngo Bao Chau

### IAS
and Columbia

*Abstract:
*

Deligne constructed
a remarkable local system on P^1 - {0, ∞} attached to a

natural family of Kloosterman sum. Katz calculated its monodromy
and asked

the questions
how to construct Kloosterman sheaves associated to general
reductive

groups and what is
the automorphic form attached to it by Langlands correspondence.

By using the trace formula, Gross proved the
existence and the unicity of automorphic

representations with
given ramification behaviour at 0 and ∞ that should
correspond to

the Kloosterman sheaf. Frenkel and
Gross also constructed a D-module that should be the

shadow of the l-adic Kloosterman sheaf that we
are looking for. In a joint work with J. Heinloth

and Z. Yun, we constructed l-adic Kloosterman sheaf for reductive group in a uniform way

via the geometric Langlands correspondence. Our construction gives a rather refreshing

example of (wild)
geometric Langlands correspondence that is not
understood in general.

**April 21th, Wednesday, 5:00-6:00 pm**

**Mathematics
520**

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