Geometric Group Theory Seminar

In Fall 2026, we will continue running Purdue Geometric Group Theory (GGT) Seminar. It will be held on Fridays 11:30 am-12:20pm Eastern Time in Math 731 if we meet in person. Some talks will be on zoom and the link will be included in the email announcement.

We are maintaining an email list for this seminar, through which we send notifications regarding talks and seminar lunches/dinners. You can subscribe to the list (choose "regular" role) by the link here: https://lists.purdue.edu/scripts/wa.exe?SUBED1=GGT-SEMINAR&A=1

Lvzhou Chen, Yash Lodha, Ben McReynolds are organizing this seminar in Fall 2026.

Past talks can be found here.

 

Fall 2026

 

September 4, 2026

Yash Lodha (Purdue)

Title: On the OpenAI construction of a non-sofic group, part I

Abstract: The class of sofic groups was introduced by Gromov as a common generalization of amenable and residually finite groups. Strikingly, sofic groups satisfy several longstanding conjectures. For a long time it was an open problem whether a non-sofic group exists, which was recently solved by OpenAI. I will provide some background and motivation for this problem, followed by a short explanation of some key ideas in the proof.

 

September 8, 2026 (Tuesday, Colloquium)

Daniel Groves (UIC)

Title: 3-manifold groups?

Abstract: Due to a vast amount of work over the last decades, the fundamental groups of 3-manifolds are by now very well understood. I will focus on the following (wide open) question: When is a discrete group the fundamental group of a compact 3-manifold? I'll discuss the background to this question, what is known in various dimensions, and then focus on the case of greatest interest in 3 dimensional topology - the hyperbolic case. Finally, I'll report on some recent work around this question in joint work with Haissinsky, Manning, Osajda, Sisto, and Walsh.

 

September 18, 2026

Yash Lodha (Purdue)

Title: On the OpenAI construction of a non-sofic group, part II

Abstract: The class of sofic groups was introduced by Gromov as a common generalization of amenable and residually finite groups. Strikingly, sofic groups satisfy several longstanding conjectures. For a long time it was an open problem whether a non-sofic group exists, which was recently solved by OpenAI. I will provide some background and motivation for this problem, followed by a short explanation of some key ideas in the proof.

 

September 25, 2026

Carolyn Abbott (Brandeis University)

Title: Random quotients of hierarchically hyperbolic groups

Abstract: Randomness is a way to discuss generic or typical behavior in a (class of) group(s).  In this talk, I will discuss random quotients of certain classes of groups.  Quotients of hyperbolic groups (groups that act geometrically on a hyperbolic space) and their generalizations have long been a powerful tool for proving strong algebraic results.  I will focus on random quotients of acylindrical and hierarchically hyperbolic groups (HHGs), two generalizations of hyperbolic groups that include mapping class groups, most CAT(0) cubical groups including right-angled Artin and Coxeter groups, many 3–manifold groups, and various combinations of such groups. In this context, I will explain why a random quotient of an HHG that does not split as a direct product is again an HHG, definitively showing that the class of HHGs is quite broad. I will also describe how the result can also be applied to understand the geometry of random quotients of hyperbolic and relatively hyperbolic groups. This is joint work with Dan Berlyne, Giorgio Mangioni, Thomas Ng, and Alexander Rasmussen.

 

October 2, 2026

Andrew Ng (University of Bonn), on zoom at: https://purdue-edu.zoom.us/j/97910559532

Title: surface subgroups in some one relator groups with torsion

Abstract: it is a longstanding open problem whether all one-ended hyperbolic groups contain a surface subgroup. One-relator groups with torsion are known to be hyperbolic, so it is natural to restrict the question to this special case. I will report on an attempt to do this using techniques developed by Wilton. It is also of interest to determine
properties of words in the free group from the profinite completion. As a corollary of the main result, we deduce a profinite criterion for words to be primitive, and for a word to be a surface word.

 

October 9, 2026

Bin Sun (MSU)

Title: Boundary cohomology and algebraic structure of relatively hyperbolic locally compact groups

Abstract: We study cohomological conditions that force a relatively hyperbolic locally compact group to be compact-by-Lie. Let G be a second-countable locally compact group, hyperbolic relative to a possibly empty finite family of open subgroups. Assume that each peripheral subgroup admits a finite proper classifying model.
Our main result concerns continuous cohomology with coefficients in the corresponding real Bruhat test-function spaces. Suppose that the relative cohomology of the group and its peripheral family is one-dimensional in degree three and vanishes in all other degrees, while the cohomology of each peripheral subgroup is one-dimensional in degree two and vanishes otherwise. If the natural maps from peripheral degree-two cohomology to relative degree-three cohomology are all nonzero, then the relative boundary is homeomorphic to the two-sphere and G is compact-by-Lie. When the peripheral family is nonempty, we obtain the stronger conclusion that G is compact-by-discrete.
A key ingredient is a locally compact version of the Bestvina–Mess boundary-cohomology isomorphism, identifying relative continuous cohomology with Bruhat test-function coefficients with the reduced Čech cohomology of the boundary, with real coefficients and a shift of one degree.

 

October 16, 2026

Yash Lodha (Purdue)

Title: On the OpenAI construction of a non-sofic group, part III

Abstract: The class of sofic groups was introduced by Gromov as a common generalization of amenable and residually finite groups. Strikingly, sofic groups satisfy several longstanding conjectures. For a long time it was an open problem whether a non-sofic group exists, which was recently solved by OpenAI. I will provide some background and motivation for this problem, followed by a short explanation of some key ideas in the proof.

 

October 23, 2026

Ino Loukidou (UChicago)

 

November 13, 2026

Inyoung Ryu (TAMU)

 

 

November 27, 2026 (No talk due to Thanksgiving)