Speaker: Sören Galatius (Kopenhagen) Title: Homeomorphisms of contractible manifolds Abstract: I will discuss joint work with Randal-Williams on contractible compact manifolds and their homeomorphism groups. In dimension $d \leq 3$, any contractible $d$-manifold is homeomorphic to the disk $D^d$, and it was proved by Alexander in 1923 that the group of all homeomorphisms of $D^d$, restricting to the identity on the boundary, is contractible. In dimension $d > 3$ there are plenty of examples of contractible compact manifolds with non-simply connected boundary, which are therefore not homeomorphic to $D^d$. In joint work with Randal-Williams we prove that, at least for $d \geq 6$, such manifolds nevertheless have contractible homeomorphism groups relative to their boundary. A key tool is embedding calculus, developed by Michael Weiss and others.