Topology and Geometric Group Theory Seminars at the Ohio State University

Aug 27 -

Sep 1 - 

Sep 3 - Francesco Lin (Columbia)

Adjunction inequalities and the Davis hyperbolic four-manifold

LeBrun conjectured that the Seiberg-Witten invariants of closed hyperbolic four-manifolds vanish. After discussing context and consequences, I will provide an overview of what is known, and then focus on the proof (joint work with Bruno Martelli) that the conjecture holds for the Davis manifold.

Sep 8 - 

Sep 10 - Yu-Chan Chang (OSU)

Isomorphism Problems for Bestvina--Brady Groups

Bestvina--Brady groups are subgroups of right-angled Artin groups, and both families of groups are defined on finite simple graphs. This talk will address two isomorphism problems concerning Bestvina--Brady groups. Specifically, I will discuss how that tree spanners and matroids come into play when answering these questions. This is joint work with Lorenzo Ruffoni.

Sep 15 - 

Sep 17 - Maya Verma (OSU)

Torsion-free lattices in Baumslag-Solitar complexes 

For the Cayley 2-complex X_{m,n}​ of a Baumslag-Solitar group BS(m,n), one can consider the group of combinatorial automorphisms, denoted Aut(X_{m,n}​). In this talk, we explore torsion-free uniform lattices in the locally compact group Aut(X_{m,n}​). We classify the pairs of nonzero integers (m,n) for which Aut(X_{m,n}​) contains torsion-free incommensurable lattices.

Sep 22 - 

Sep 24 - Yukun Du (University of Georgia)

Two-Generator Discrete Subgroups of Tree Automorphism Groups

I will discuss the classification of discrete two-generator groups acting on locally finite trees. Under a small-geometry condition, the possible groups and quotient graphs are strongly constrained and can be classified explicitly. I will then explain how the picture becomes much richer beyond this regime, including higher-index amalgams and families with arbitrarily complicated quotient geometry.

Sep 29 - 

Oct 1 -

Oct 6 -

Oct 8 - Zhihao Mu (CUNY)

Connectivity of boundaries of right-angled Coxeter groups 

A central theme in geometric group theory is to study finitely generated groups through their large-scale geometry. Right-angled Coxeter groups (RACGs) are defined by finite graphs, and much of their large-scale geometry is visible in the combinatorics of these defining graphs. To each RACG, we can canonically associate a hyperbolic space, obtained by coning-off flats in its Davis complex. In this talk, I will characterize, in terms of combinatorics of the defining graph, when the Gromov boundary of this hyperbolic space is connected. Moreover, whenever the boundary is connected, it is also linearly connected. As an application, among one-ended RACGs, the existence of a splitting over a subgroup contained in a direct product of two infinite subgroups is preserved by quasi-isometries. 

Oct 13 - Chloé Postel-Vinay (U Chicago)

Oct 15 - Autumn Break

Oct 20 - 

Oct 22 - Matt Zaremsky (SUNY Albany)

Finitely presented simple groups, and the state of the art of the Boone-Higman conjecture 

In the 1970's, Boone and Higman conjectured that every finitely generated group with solvable word problem embeds in a finitely presented simple group. In this talk I will discuss recent progress on this conjecture, and highlight the important role played by a certain family of generalizations of Thompson's group V. In particular, in recent joint work with Francesco Fournier-Facio and Xiaolei Wu, we prove that whenever a group satisfies the Boone-Higman conjecture, it also satisfies a related embedding conjecture entirely in the world of Thompson-like groups. This talk will also touch on joint work with Jim Belk and James Hyde.

Oct 27 - Meenakshy Jyothis (U of Oklahoma)

Oct 29 - 

Nov 3 - Manisha Garg (UIUC)

Nov 5 - Emily Stark (Wesleyan)

Nov 10 - 

Nov 12 - Christopher Cericola (Oregon State)

Nov 17 - Rado Lectures

Nov 19 - 

Nov 24 - Amy Tao (UW-Madison)

Nov 26 - Thanksgiving break

Dec 1 - 

Dec 3 - 

Dec 8 -