Abstract：

The topological group of homeomorphisms of d-dimensional Euclidean space is a basic object in geometric topology, closely related to understanding the difference between diffeomorphisms and homeomorphisms of all d-dimensional manifolds (except when d=4). I will explain some methods that have been used for studying the algebraic topology of this group, and report on a recently obtained conjectural picture of it.

Bio：

Oscar Randal-Williams (https://www.dpmms.cam.ac.uk/~or257/) is a Professor of Mathematics at the Department of Pure Mathematics and  Mathematical Statistics of the University of Cambridge. He is  interested in algebraic and geometric topology, in particular the topology of moduli spaces, automorphism groups of manifolds, and applications of homotopy theory to geometry. He has been awarded the Whitehead prize, the Philip Leverhulme prize, the Dannie Heineman prize, the Oberwolfach prize, and most recently the Clay Research Award.