Topology & Group Theory Seminar

Vanderbilt University


Links to seminar schedule for previous years:
2010/11, 2011/12, 2012/13, 2014/15, Spring 2016, Fall 2016, Spring 2017, 2017/18, 2018/19

Organizer: Spencer Dowdall

Wednesdays, 4:10–5:00pm in SC 1308 (unless otherwise noted)

Wednesday, August 28, 2019

Kevin Schreve (University of Chicago)

Title: Proper actions versus uniform embeddings

Absract: Whenever a finitely generated group \(G\) acts properly discontinuously by isometries on a metric space \(X\), there is an induced uniform embedding (a Lipschitz and uniformly proper map) \(f \colon G\to X\) given by mapping \(G\) to an orbit. I will talk about some examples of groups which uniformly embed into a contractible n-manifold but do not act on a contractible n-manifold. Kapovich and Kleiner constructed torsion-free hyperbolic groups that embed into \(\mathbb{R}^3\) but only act on \(\mathbb{R}^4\). My main application will be showing that certain k-fold direct products of these groups do not act on \(\mathbb{R}^{3k}\).

Wednesday, September 4, 2019

Matthew Haulmark (Vanderbilt)

Title: Canonical JSJ for Relatively Hyperbolic Groups

Abstract: JSJ decompositions first appeared in the context of 3-manifolds with the work of Jaco-Shalen and Johannson. Generalizations of JSJ theory to finitely generated groups have been studied in different contexts by many authors (Kropholler, Rips-Sela, Papasoglu-Swenson, Bowditch, Guirardel-Levitt, etc.). Guirardel and Levitt have shown that if G is one ended and hyperbolic relative to a finite collection of finitely generated subgroups, then there is a relative JSJ tree for G over the class of elementary subgroups. In a joint work with Chris Hruska we show that Guirardel and Levitt’s result can be obtained from the topology of the Bowditch boundary. This implies that the relative JSJ tree for G is a “relative” quasi-isometry invariant.

Wednesday, September 11, 2019

No Seminar

Wednesday, September 18, 2019

Simon Andre (Vanderbilt)

Title: Hyperbolicity is preserved under elementary equivalence

Abstract: Zlil Sela proved that a finitely generated group that satisfies the same first-order properties as a torsion-free hyperbolic group is torsion-free hyperbolic. I will explain that this result remains true for hyperbolic groups with torsion, as well as for subgroups of hyperbolic groups, and for hyperbolic and cubulable groups.

Wednesday, September 25, 2019

Rachel Skipper (OSU)

Title: Finiteness Properties for Simple Groups

Abstract: A group is said to be of type $F_n$ if it admits a classifying space with compact \(n\)-skeleton. We will consider the class of Röver-Nekrachevych groups, a class of groups built out of self-similar groups and Higman-Thompson groups, and use them to produce a simple group of type \(F_{n-1}\) but not \(F_n\) for each \(n\). These are the first known examples for \(n\geq 3\). As a consequence, we find the second known infinite family of quasi-isometry classes of finitely presented simple groups.

Wednesday, October 16, 2019

Jean Pierre Mutanguha (Arkansas)

Title: The irreducibility of monodromy is a mapping torus invariant

Abstract: An immediate corollary of Nielsen-Thurston classification of surface homeomorphisms is that if two surface homeomorphisms f and g have homeomorphic mapping tori, then f is pseudo-Anosov if and only if g is pseudo-Anosov. Using hyperbolization theorem and rigidity results, the hypothesis can be weakened to quasi-isometric mapping tori. We show an analogous result for free group automorphisms: if two free group automorphisms have isomorphic mapping tori, then the first automorphism is fully irreducible and atoroidal if and only if the other is fully irreducible and atoroidal. This answers a question posed by Dowdall-Kapovich-Leininger.

Wednesday, October 23, 2019

Levi Sledd (Vanderbilt)

Title/Abstract: TBA

Wednesday, November 6, 2019

Daniel Studenmund (Notre Dame)

Title/Abstract: TBA

Wednesday, November 13, 2019

Lauren Ruth (Vanderbilt)

Title/Abstract: TBA

Wednesday, November 20, 2019

Jason Behrstock (CUNY)

Title/Abstract: TBA

Wednesday, November 27, 2019

No Seminar (Thanksgiving break)

Wednesday, January 8, 2020

Genevieve Walsh (Tufts)

Title/Abstract: TBA

Wednesday, March 4, 2020

No Seminar (Spring Break)

Wednesday, March 25, 2020

Michael Hull (University of North Carolina, Greensboro)

Title/Abstract: TBA

Wednesday, April 22, 2020

No Seminar (Start of summer holiday)