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.