** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2016.01.19, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Geometry of hierarchically hyperbolic spaces."

**Speaker:** Mark Hagen (University of
Cambridge)

**Abstract:**
Hierarchically hyperbolic spaces are a class of spaces defined
by abstracting various properties of the mapping class group of a
surface; roughly, they are spaces whose geometry is encoded by their
projections onto a specified, organized collection of Gromov-hyperbolic
metric spaces. As well as mapping class groups, this class includes
many groups acting on CAT(0) cube complexes, including all virtually
compact special groups, most 3-manifold groups, etc. In this talk, I'll
discuss the definition and certain "coning" constructions that enable
one to study asymptotic invariants and to build a small-cancellation
theory over hierarchically hyperbolic groups.