Joint IAS/Princeton University Symplectic Geometry Seminar

While much is known about the algebraic structure of the group of volume preserving homeomorphisms of a manifold when the dimension of the manifold is at least three, the structure of these groups in the two-dimensional case has long been mysterious. I will explain some recent progress in understanding the two-dimensional case, while also highlighting some mysteries that remain. More precisely, I will discuss my recent joint work in arXiv:2206.10749, finding a plethora of new normal subgroups by studying the asymptotics of ``link spectral invariants"; we answer in particular old questions of Oh-Mueller and Fathi. A conjectural "two-term Weyl law" plays a key role in our arguments, and I will explain this conjecture along with some partial progress.