**Michael Lennox Wong**

TIFR

November 4, 2010

**Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles**:
A Hecke modification of a holomorphic principal bundle over a Riemann
surface is obtained by twisting the transition function in a neighbourhood of a point. The spaces of such modifications can be described in terms of the Bruhat cells of the associated affine Grassmannian. Thus, one can form families of principal bundles parametrized by such spaces. When the group is semisimple of adjoint type, one can use the wonderful (De Concini-Procesi) compactification to obtain parametrizations of the moduli space of bundles in certain cases. The aim of this talk will be to describe the constructions just mentioned and to outline how the parametrization is obtained.