# Mathematical Sciences Research Institute

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# Seminar

Coarse embeddings, and how to avoid them November 30, 2016 (10:00 AM PST - 11:00 AM PST)
Parent Program: Geometric Group Theory MSRI: Baker Board Room
Speaker(s) David Hume (Université de Paris XI)
Description No Description
Video
Abstract/Media

Coarse embeddings occur completely naturally in geometric group theory: every finitely generated subgroup of a finitely generated group is coarsely embedded. Since even very nice classes of groups - hyperbolic groups or right-angled Artin groups for example - are known to have 'wild' collections of subgroups, there are precious few invariants that one may use to prove a statement of the form '$H$ does not coarsely embed into $G$' for two finitely generated groups $G,H$.

The growth function and the asymptotic dimension are two coarse invariants which which have been extensively studied, and a more recent invariant is the separation profile of Benjamini-Schramm-Timar.

In this talk I will describe a new spectrum of coarse invariants, which include both the separation profile and the growth function, and can be used to tackle many interesting problems, for instance: Does there exist a coarse embedding of the Baumslag-Solitar group $BS(1,2)$ into a hyperbolic group?

This is part of an ongoing collaboration with John Mackay and Romain Tessera.