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Texas A&M University
Mathematics

Events for 10/28/2020 from all calendars

Probability Seminar

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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

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Time: 4:00PM - 5:00PM

Location: zoom

Speaker: Paul VanKoughnett, Purdue University

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