Groups and Dynamics Seminar

Date: October 20, 2021

Time: 3:00PM - 4:00PM

Location: online

Speaker: Heejoung Kim , Ohio State University

Title: Algorithms detecting stability and Morseness for finitely generated groups

Abstract: In geometric group theory, finding algorithms for detection and decidability of various properties of groups is a fundamental question. For a finitely generated group G, we can study not only algorithmic problems for G itself but also algorithms related to a particular class of subgroups. For a word-hyperbolic group G, quasiconvex subgroups have been studied widely and there are algorithmic results. For example, Kapovich provided a partial algorithm which, for a finite set S of G, only halts if S generates a quasiconvex subgroup of G. 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, and toral relatively hyperbolic groups.