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.
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: Calabi-Yau metrics and optimal transport
Abstract: Recent development in the study of Calabi-Yau metrics have revealed an intriguing connection with the theory of optimal transport, namely that Calabi-Yau metrics in certain degenerate and asymptotic regimes are often described by solutions to optimal transport problems. In this talk, I will discuss some recent advances in the regularity theory of optimal transport maps and its relationship with problems in Kahler geometry. Based on joint works with T. Collins and S.-T. Yau.
Title: Complex Monge-Ampere equations from geometric flows
Abstract: We present various setups where natural geometric flows lead to Monge-Ampere flows when the flow is started with suitable initial data. Examples include the G2 Laplacian flow on 7-manifolds, the hypersymplectic flow on 4-manifolds, the anomaly flow on Calabi-Yau 3-folds, and Type IIA flow on symplectic 6-manifolds.
Title: The second rational homology group of the Torelli group
Abstract: After giving an introduction to finiteness properties of the mapping class group and its subgroups, I will discuss a recent theorem I proved with Minahan calculating the second homology group of the Torelli group.
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.