- Speaker: Prof. Andrew Zimmer (William and Mary University)

- Abstract: 

For certain classes of bounded domains we give a precise description of the automorphism group and its limit set in the boundary. For instance, for finite type pseudoconvex domains we prove: if the limit set contains at least two different points, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to Aut (B_k). Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2k-1. For convex domains with C^1,ε boundary we can prove a similar result. In this talk we will describe the main ideas of the proofs and discuss some applications.