## Mathematics Department Colloquium: Geometry, dynamics, and the moduli space of Riemann surfaces

Colloquium | September 21 | 4:10-5 p.m. | 60 Evans Hall

Alex Wright, Stanford University

Department of Mathematics

One of the themes of Maryam Mirzakhani's work is that the dynamics and geometry of individual surfaces are closely tied to moduli spaces of surfaces. Starting from this general perspective, we will focus in on our recent joint work with Mirzakhani and others on the $\mathbf {GL}(2, {\bf R} )$ action on the Hodge bundle over the moduli space of Riemann surfaces. This action will be presented in a very elementary way in terms of polygons in the plane. We will mention some of the deep connections to other subjects, and will likely touch on joint work with Eskin, Filip, McMullen, and Mukamel.

Our talk is intended for a broad audience.

ribet@berkeley.edu