# The $\mathrm{SL}(2,\mathbb R)$ action on moduli space

 Members' Seminar Topic: The $\mathrm{SL}(2,\mathbb R)$ action on moduli space Speaker: Alex Eskin Affiliation: University of Chicago; Member, School of Mathematics Date: Monday, November 16 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: https://video.ias.edu/membsem/2015/1116-Eskin

There is a natural action of the group $\mathrm{SL}(2,\mathbb R)$ of $2 \times 2$ matrices on the unit tangent bundle of the moduli space of compact Riemann surfaces. This action can be visualized using flat geometry models, which allows one to make an analogy with homogeneous spaces, such as the space of lattices in $\mathbb R^n$. I will make the basic definitions, and mention some recent developments. This talk will be even more introductory than usual.