Punctured mapping class group actions on the circle

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.