Geometric Group Theory Seminar
In Fall 2026, we will continue running Purdue Geometric Group Theory (GGT) Seminar. It will be held on Fridays 11am-noon 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.
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)
October 9, 2026
Bin Sun (MSU)
October 23, 2026
Ino Loukidou (UChicago)
November 13, 2026
Inyoung Ryu (TAMU)
November 27, 2026 (No talk due to Thanksgiving)