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Explore various methods for proving functional inequalities in hypoelliptic diffusions and heat kernels in this 56-minute lecture. Delve into geometric approaches like curvature-dimension inequalities developed by Baudoin-Garofalo, as well as probabilistic techniques such as couplings. Gain insights into recent applications of these methods to ergodicity in Langevin dynamics. Learn from the collaborative research of Masha Gordina, F. Baudoin, B. Driver, T. Melcher, Ph. Mariano, and others in this comprehensive overview of stochastic analysis and geometric functional inequalities presented at the Hausdorff Center for Mathematics.
