# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Harmonic measure and rigidity for surface group actions on the circle"

In 1990s, Frankel and Thurston independently proposed alternative proofs for the Milnor-Wood inequality based on foliated harmonic measures. In particular, Frankel pointed out that Matsumoto's rigidity theorem directly follows from his argument. Revisiting their approach, we shall give a harmonic measure proof for a theorem of Burger, Iozzi and Weinhard: a Milnor-Wood type inequality and a Matsumoto type rigidity theorem for actions of torsion-free, but not necessarily cocompact, lattices of $\operatorname{PSL}(2;\mathbb{R})$ on the circle. This is joint work with Yoshifumi Matsuda (Aoyama Gakuin University) and Hiraku Nozawa (Ritsumeikan University).