Holonomy representations which are a diagonal direct sum of two faithful representations

We study holonomy representations admitting a pair of supplementary faithful sub-representations. In particular the cases where the sub-representations are isomorphic respectively dual to each other are treated. In each case we have a closer look at the classification in small dimension

Infinitesimal semisimple symplectic extrinsic symmetric spaces

We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case

Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in \CC^n, $n > 1$, with Lipschitz boundary, but it holds for domains in \CC^1 with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergman curvature, stability properties for the Bergman kernel, and also some ideas about equivariant embeddings

The corona problem with two pieces of data

We study the corona problem on the unit ball in \CC^n, and more generally on strongly pseudoconvex domains in \CC^n. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able to solve it