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

The SL(2,ℝ) action on moduli space - Alex Eskin

Alex Eskin
University of Chicago; Member, School of Mathematics
November 16, 2015
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.