Modul: MAT772 Geometrie-Seminar

## Approaching quasi-isometry classification of Lie groups using isometries

Ville Kivioja talk

Speaker invited by: Prof. Dr. Viktor Schroeder

**Date:** 20.11.19 **Time:** 15.45 - 16.45 **Room:** ETH HG G 43

The talk is motivated by searching strategies to attack the conjecture stating that if two simply connected nilpotent Lie groups are quasi-isometric, they must be isomorphic. This conjecture has a related cousin for Heintze groups, and these conjectures also give rise to questions of the following type: Given two Lie groups, when does it actually happen that one can find left-invariant distances on them such that they become isometric as metric spaces. I will give some answers to these questions, concentrating on groups of polynomial growth on the one hand, and on Heintze groups on the other. Finally I will remark how Lie groups with left-invariant distances appear naturally in metric geometry as model spaces for homogeneous metric spaces, and sometimes as their visual boundaries.