Iordan Ganev, IST Austria
"The wonderful compactification for quantum groups"
The wonderful compactification of a group plays a crucial role in several areas of geometric representation theory and related fields. In this talk, we will give a construction of the wonderful compactification and explain how its rich structure links the geometry of the group to the geometry of its partial flag varieties. We will describe several examples in detail. The wonderful compactification of a group also encodes the asymptotics of matrix coefficients for the group and captures the rational degenerations of the group. We will explain a construction of the wonderful compactification via the Vinberg semigroup which makes these properties explicit. We will then introduce quantum group versions of the Vinberg semigroup, the wonderful compactification, and the latter's stratification by G x G orbits. Our approach relies on a theory of noncommutative projective schemes, which we will review briefly.