Topology & Group Theory Seminar

Vanderbilt University

2014/2015

Organizer: Mark Sapir

Wednesdays, 4:10pm in SC 1310 (unless otherwise noted)

** Wednesday, August 27, 2014 **

Speaker: Ashot Minasyan (Southampton, UK)

Title: On universal right angled Artin groups.

Abstract: A right angled Artin group (RAAG), also called a graph group or a partially commutative group, is a group which has a finite presentation where the only permitted defining relators are commutators of the generators. These groups and their subgroups play an important role in Geometric Group Theory, especially in view of the recent groundbreaking results of Haglund, Wise, Agol, and others, showing that many groups possess finite index subgroups that embed into RAAGs.

In their recent work on limit groups over right angled Artin groups, Casals-Ruiz and Kazachkov asked whether for every natural number n there exists a single "universal"
RAAG, A_n, containing all n-generated subgroups of RAAGs. Motivated by this question, I will discuss several results showing that "universal" (in various contexts) RAAGs generally do not exist.

**Wednesday, September 3, 2014 **

Speaker: Gili Golan (Bar Ilan, Israel)

Title: Tarski numbers of group actions

Abstract: The Tarski number of an action of a group G on a set X is the minimal number of pieces in a paradoxical decomposition of it. For any k > 3 we construct a faithful transitive group action with Tarski number k. Since every k<4 is not a Tarski number, this provides a complete characterization of Tarski numbers of group actions. Using similar techniques we construct a group action of a free group F with Tarski number 6 such that the Tarski numbers of restrictions of this action to finite index subgroups of F are arbitrarily large.

** Wednesday, September 17, 2014 **

Speaker: Mike Mihalik (Vanderbilt)

Title: TBA

Abstract: TBA

** Wednesday, October 15, 2014 **

Speaker: Andrew Sale (Vanderbilt)

Title: TBA

Abstract: TBA