## Dynamics, Geometry, & Groups - Heejoung Kim (UIUC)

### Thursday, October 17th, 2019

**Time:** 3:30 p.m** Place:** Jeffery Hall 319

**Speaker:** Heejoung Kim (University of Illinois, Urbana-Champaign)

**Title:** Algorithms detecting stability and Morseness for finitely generated groups.

**Abstract:** For a word-hyperbolic group G, the notion of quasiconvexity is independent on the choice of a generating set and a quasiconvex subgroup of G is quasi-isometrically embedded in G. Kapovich provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise. However, beyond word-hyperbolic groups, the notion of quasiconveixty is not as useful. For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, a ``stable'' subgroup and a ``Morse'' subgroup. In this talk, we will discuss various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups.