### Uhlenbeck compactifications as a stack

**Baranovski, V ***(California)*

Saturday 18 April 2009, 10:30-11:00

Satellite

#### Abstract

I will explain how the Uhlenbeck compactification of vector bundles on a smooth projective surface can be defined as a functor of families (i.e. as an algebraic stack). I will also explain how Hecke correspondences which modify a vector bundle along a divisor on a surface, can be extended to the Uhlenbeck compactification. This construction is related to the conjectural higher dimensional Geometric Langlands program