**
Edward Witten
**

**Gauge theory and the Geometric
Langlands Program.
**

**Abstract
**

*N=4* super Yang-Mills theory in four dimensions, compactified to
two dimensions on a Riemann surface *C*, gives, via its
*S*-duality symmetry, a natural framework for understanding the
geometric Langlands program for complex Riemann surfaces. The
correspondence between the tensor algebra of representations of
* ^{L}G* and the Hecke algebra of