Columbia Mathematics Department Colloquium


Kloosterman sheaves for reductive groups


  Ngo Bao Chau  

IAS and Columbia



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