Fri, Dec 6

Geometry and Topology Seminar
Robbie Lyman (Rutgers University)
Geometries for groups


4:00PM, 122 Mathematics Building

I want to introduce to you the space and poset of metric structures on a fixed topological group; this is an initially unusual formulation of the fundamental structures in geometric group theory, but I’m hoping that it will make some things click for you in the way it did for me. It’s well-suited to addressing questions such as “when does a group have a quasi-isometry type?” or “supposing a group has a quasi-isometry type, does it receive that type via an isometric action on a graph?” As an application, I’d also like to discuss joint work with Beth Branman, George Domat and Hannah Hoganson. In this work we use actions on graphs to compute the quasi-isometry type (and whether it exists) of the group of homeomorphisms of a space E, where E is required to be countable, compact Hausdorff and totally disconnected.

Mon, Dec 9

Algebra Seminar
Ankit Rai, UB
Perverse filtrations via Brylinski-Radontransformations 
4:00PM, University at Buffalo Mathematics room 250

Perverse sheaves are certain complexes ofconstructible sheaves invented by Goresky-MacPherson in 1983. This talk will becentered around the topic of (middle) perverse sheaves and more generally ont-structure(s) on the derived category of constructible sheaves on an algebraicvariety \(X\) defined over a field \(\Bbbk\). A t-structure gives rise to truncation functors and hence a cohomologytheory which takes values in the abelian category of perverse sheaves. A complex\(K\) of constructible sheaves on \(X\) can be filtered using these truncationfunctors, in turn inducing a filtration on the (hyper)cohomology of the complex\(K\). In 2010, deCataldo-Migliorini proved a result which explains thisfiltration geometrically. In recent work with K. V. Shuddhodan we show thattheir result can be upgraded to an equality at the level of sheaves and is acorollary of the t-exactness of a certain Brylinski-Radon transform. Ourarticle is available at\url{https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fabs%2F2309.13973&data=05%7C02%7Cmahacker%40buffalo.edu%7C5736ed01c1074aa5440d08dd057a5ad9%7C96464a8af8ed40b199e25f6b50a20250%7C0%7C0%7C638672745243619201%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=qqWc%2FvNYGJbvfPQvJTnMhCvWOoAxl5OWQ3lWtXGIDdM%3D&reserved=0}.

Wed, Jan 22

Analysis Seminar
Guo Chuan Thiang, Peking University
4:00PM, 250 Math Building