David Fisher

Abstract:   By a non-linear representation of a finitely generated group G, we mean an action of G on a smooth compact manifold M by volume preserving diffeomorphisms. In other words, a homomorphism from G into Diff_omega(M). Ideally, one would like to classify non-linear representations, at least for large enough G and small enough M. I will survey a wide variety of results and techniques for approaching this problem, before concentrating on my recent joint work with Margulis. In this work, we consider the question of rigidity of non-linear representations of both higher rank lattices and, more generally, groups with property T of Kazhdan. We call a non-linear representation rigid if any perturbation is conjugate back to the original representation.