Published on *Department of Mathematics* (https://math.yale.edu)

March 26, 2019 - 4:15pm

DL 431

The mapping class group of a surface S with a marked point can

be identified with the group $Aut(\pi_1(S))$ of automorphisms of the

fundamental group of the surface. I will explain a new rigidity theorem,

joint with M. Wolff, that shows that any nontrivial action of $Aut(\pi_1(S))$

on the circle is semi-conjugate to its natural action on the Gromov

boundary of $\pi_1(S)$; solving a problem posed by Farb. As a consequence, we

can also quickly recover and extend some older results on the regularity

(non-smoothability) of these group actions.