Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Deligne-Mostow lattices: fundamental domains and line arrangements

Talk by Dr. Irene Pasquinelli

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 21.10.20 **Time:** 10.30 - 11.30 **Room:** Y27H28

We will talk about lattices in the group PU(n,1) of holomorphic isometries of complex hyperbolic space. A well known class is that of the Deligne-Mostow lattices. I will describe different interpretations of these lattices and explain how one can use Thurston's interpretation to build fundamental domains for them. Then I will explain how Hirzebruch's line arrangements construction of the Deligne-Mostow lattices is related to the fundamental domains. Finally I will tell you how we used this connection to go a step forward towards giving a complex equivalent to the hybrid construction. Part of these results are in a joint work with Elisha Falbel.