This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assuming resolution of singularities (for example complex varieties). The slogan is that every variety is locally smooth in this topology. Adapting this to algebraic K-theory has led to several breakthroughs in computation, and clarified connections between the "singular" part of K-theory and Hodge theory.
In this seminar, we will discuss the recent work on the eigenvalue and eigenvector distributions of random matrices. We will discuss a dynamical approach to these problems and related open questions. We will discuss both Wigner type matrix ensembles and invariant ensembles.
In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The talk will present the developments which arose from Lichnerowicz's question. It will be an opportunity to see diverse aspects of conformal dynamics in Riemannian, as well as Lorentzian geometry