## Dynamics, Geometry, & Groups Seminar

### Friday, March 6th, 2020

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Merlin Incerti-Medici (Universität Zürich)

**Title:** Circumcenter extension maps for Hadamard manifolds.

**Abstract:** Given a geodesically complete CAT(-1) space, we can associate a boundary at infinity to it. This boundary is equipped with a geometric structure called cross ratio. While it was known for several decades that the boundary together with the cross ratio completely determines the interior space in some special cases, we recently learned that they always roughly determine the interior space. The key tool in this process is a construction called the circumcenter extension. In this talk, we survey known results about the circumcenter extension and show that its construction can be performed in a large class of CAT(0) spaces and still yields interesting results.