Ismael Sierra: Homological stability of diffeomorphism groups using E_k algebras

Abstract

I will state some recent results about homological stability of diffeomorphism groups of manifolds and give an outline of their proof. In particular, I will talk about the connection to E_k algebras, and about certain complexes, called "splitting complexes", whose high-connectivities are essential to the proof. Finally I will sketch the proof of the high-connectivity of the splitting complexes, which is the most substantial part of the whole argument.