Date/Time
Date(s) - 22/11/2024
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 305

Speaker: Danny Ruberman (Brandeis University)
Research Area: Gauge theory, topology of manifolds

Title: Diffeomorphism groups of 4-manifolds

Abstract: The group of diffeomorphisms, Diff(X) of a smooth manifold X is an interesting topological space in its own right. Basic algebraic topological invariants of Diff(X) encode non-trivial information; for instance the path-components of the diffeomorphism group of a n-dimensional sphere (for n at least 6) turn out to be the same as the set of smooth structures on the (n+1)-dimensional sphere. I will discuss recent developments that show that the diffeomorphism group of a 4-dimensional manifold has very complicated algebraic topology, including infinitely generated homotopy groups. The underlying idea is to study families of 4-manifolds using the Seiberg-Witten equations.

Coffee will be served in the same room, HH 305 at 3pm. All are welcome.