Mathematics Colloquium: The algebraic structure of groups of area-preserving homeomorphisms of surfaces

Speaker:  Daniel Cristofaro-Gardiner, University of Maryland

Title: The algebraic structure of groups of area-preserving homeomorphisms of surfaces

Abstract:   The algebraic structure of the group of volume-preserving homeomorphisms of a manifold of dimension at least 3 has been well-understood since the work of Fathi from the 70s.  However, the surface case has long remained a mystery.  I will explain some recent joint works clearing up parts of this mystery.  A main point is a way of defining the "average rotation" of an area-preserving disc homeomorphism by using ideas from symplectic geometry.  I will also survey some of the open questions that remain.  Time permitting, I also want to briefly introduce some related very recent work of Edtmair-Seyfaddini that defines a "helicity" for exact non-singular volume-preserving topological flows.

Time:  Friday, September 12, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person