**Radhika Ganapathy**

University of British Columbia, Canada

September 4, 2014

**The Deligne-Kazhdan theory and its applications to the local Langlands correspondence**:
The Deligne-Kazhdan theory can be loosely stated as follows:
The ``complex'' representation theory of Galois groups and split reductive groups over a local field of characteristic p can be viewed as the ``limit'' of the representation theory of these groups over local fields of characteristic 0 with the same residue field, as the ramification index tends to infinity.
In this talk, we will begin by briefly reviewing this theory. We will see how this technique, combined with the work of Gan-Takeda on the local Langlands correspondence (LLC) for GSp(4,F) for local fields F of characteristic 0, can be used to prove the LLC for GSp(4,F') for a local function field F' of odd characteristic.