Fernando Pena Vazquez: Non-commutative geometric methods in the representation theory of p-adic Lie groups

The  Hochschild homology groups are one of the most important tools in the theory of  associative algebras, with applications ranging from deformation theory, to K-theory and differential geometry.  In this talk, we will construct versions of Hochschild and cyclic homology that are adapted to algebras with an analytic structure (i.e. Banach, Fréchet ...), and that present good functorial properties. To this end, we will review the concept of quasi-abelian category, and showcase how it can be used to obtain a theory of derived functors in the analytic setting. We finish the talk by discussing some calculations relevant to the theory of p-adic Lie groups.