The Geometry and Geometric Analysis Seminar at Purdue in Fall 2025 is usually on Mondays 11:30am-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.Â
Lvzhou Chen, Mathew George, and Nicholas McCleerey are organizing this seminar in Fall 2025. If you have any questions or would like to suggest speakers, please contact one of us. If you would like to be on the mailing list, please email Lvzhou.
Title: Geometric Properties of Similarity Structure Groups
Abstract: Countable Similarity Structure (CSS) groups are a certain type of discrete homeomorphism group of a compact ultrametric space that act by local similarity. They are essentially due to Farley and Hughes and are a generalized class of Thompson groups. I will introduce CSS* groups, a certain subclass that includes the Higman-Thompson groups $V_{d,r}$ and prove that CSS* groups are non-inner amenable and not acylindrically hyperbolic. Throughout the talk I will provide background on both properties and, time permitting, discuss their connections to operator algebras. This is joint work with Eli Bashwinger.
Title: Non Vanishing of the Fourth Bounded Cohomology of Free Groups and Codimension 2 Subspaces
Abstract: Bounded cohomology is a powerful albeit very hard to compute invariant. Nothing encapsulates that more than the as of yet mysterious bounded cohomology of free groups. During this talk I will give a very brief introduction to bounded cohomology, further motivate why one should care about the bounded cohomology of free groups and then explain how to show that it is non-zero in degrees two, three and four.