Events for 10/28/2020 from all calendars

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Matthew Lorentz, University of Hawai‘i at Mānoa

Title: The Hochschild cohomology of uniform Roe algebras

Abstract: Recently Rufus Willett and I showed that all bounded derivations on Uniform Roe Algebras associated to a bounded geometry metric space X are inner in our paper “Bounded Derivations on Uniform Roe Algebras”. This is equivalent to the first Hochschild cohomology group $H^1(C^*_u(X), C^*_u(X))$ vanishing. It is then natural to ask if all the higher groups $H^n(C^*_u(X), C^*_u(X))$ vanish. To investigate the continuous cohomology of a Uniform Roe Algebra we employ the technique of “reduction of cocycles” where we modify a given cocycle by a coboundary to obtain certain properties. I will discuss this procedure and give examples of calculating the higher cohomology groups.

URL: Event link

Probability Seminar

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Qi Feng, University of Southern California (USC)

Title: Entropy dissipation for degenerate diffusion process

Abstract: A drift-diffusion process with non-degenerate diffusion coefficient matrix posseses good properties (under certain conditions): convergence to equilibrium, entropy dissipation rate, etc. The degenerate drift-diffusion process possesses degenerate/rectangular diffusion coefficient matrix, which makes it difficult to govern the convergence property and entropy dissipation rate by drift-diffusion coefficients on its own because of lacking control for the system. In general, the degenerate drift-diffusion is intrinsically equipped with sub-Riemannian structure defined by the diffusion coefficients. We propose a new methodology to systematically study general drift-diffusion process through sub-Riemannian geometry and Wasserstein geometry. We generalize the Bakry-Emery calculus and Gamma z (Baudoin-Garofalo) calculus to define a new notion of sub-Riemannian Ricci curvature tensor. With the new Ricci curvature tensor, we are able to establish generalized curvature dimension bounds on sub-Riemannnian manifolds which goes beyond step two condition. As application, for the first time, we establish analytical bounds for logarithmic Sobolev inequalities for the weighted measure in a compact region on displacement group(SE(2)). Our result also provides entropy dissipation rate for Langevin dynamics with gradient drift and variable temperature matrix. The talk is based on joint works with Wuchen Li.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: zoom

Speaker: Paul VanKoughnett, Purdue University

Title: Topological modular forms and their co-operations

Abstract: Topological modular forms (TMF) is a cohomology theory built out of elliptic curves. I'll describe what TMF is, how it's constructed, and how it's been useful in topology, as well as some of the more speculative recent attempts to extend its construction. I'll then talk about the problem of calculating TMF co-operations, which are an essential input to serious computations using TMF. Part of this object -- the part that is obtained from ordinary elliptic curves -- admits a simple algebraic description, as well as an interesting relationship with number theory. This is joint work with Dominic Culver.

Student/Postdoc Working Geometry Seminar

Time: 11:00PM - 12:00PM

Location: zoom

Speaker: JM Landsberg, TAMU

Title: A technical lemma of Friedland