David Fischer: Cohomology, Compactness and Rigidity

One can characterize property (T) in terms of vanishing of the first cohomology with coefficients in any unitary representation. It is often useful that this turns out to be equivalent to vanishing of the reduced cohomology, which is a priori weaker. I will discuss a far reaching generalization of this phenomenon, that applies to many families of representations and to cohomology in all degrees. If time permits, I will also discuss motivation from and applications to the study of rigidity of group actions and to the cohomology of Lie groups and their lattices.