Sobhan Seyfaddini - The algebraic structure of groups of area-preserving homeomorphisms

July 23, 12 pm ET: Sobhan Seyfaddini (Jussieu), The algebraic structure of groups of area-preserving homeomorphisms

Abstract: I will review recent joint work with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak and Ivan Smith constructing a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, we resolve several open questions from topological surface dynamics and continuous symplectic topology:

1. We show that the group of Hamiltonian homeomorphisms of any compact surface with (possibly empty) boundary is not simple

2. We extend the Calabi homomorphism to the group of Hameomorphisms constructed by Oh-Müller.

3. We construct an infinite dimensional family of quasimorphisms on the group of area and orientation preserving homeomorphisms of the two-sphere.