## Department Colloquium

### Friday, September 27th, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Kathryn Mann (Cornell University)

**Title:** Structure theorems for actions of homeomorphism groups.

**Abstract: ** The groups $\mathrm{Homeo}(M)$ and $\mathrm{Diff}(M)$ of homeomorphisms or diffeomorphisms of a manifold $M$ have many striking parallels with finite dimensional Lie groups. In this talk, I'll describe some of these, and explain new work, joint with Lei Chen, that gives an orbit classification theorem and a structure theorem for actions of homeomorphism and diffeomorphism groups on other spaces, analogous to some classical results for actions of locally compact Lie groups. As applications, we answer many concrete questions towards classifying all actions of $\mathrm{Diff}(M)$ on other manifolds (many of which are nontrivial, for instance $\mathrm{Diff}(M)$ acts naturally on the unit tangent bundle of $M$...) and resolve several threads in a research program initiated by Ghys. I'll aim to give both a broad overview and several toy applications in the talk.

**Professor Kathryn Mann** received her PhD from the University of Chicago in 2014, she then held post-doctoral positions at MSRI, UC Berkeley and the Institut de mathématiques de Jussieu before becoming a Manning Assistant Professor of Mathematics at Brown University. In 2019, she joined Cornell University. Among her accolades is an Alfred P. Sloan Foundation Fellowship (2019), an NSF Career Award (2019), the AWM-Birman Research Prize in Topology and Geometry (2019), the Kamil Duszenko Award (2019) and the Mary Ellen Rudin young researcher award (2017).