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This lecture is the second part of a four-part series on the regularity theory of kinetic equations with rough coefficients, presented by Clément Mouhot from the University of Cambridge. Explore the extension of De Giorgi (1958) and Nash (1959) theory to hypoelliptic PDEs in kinetic theory, focusing on the Kolmogorov equation with rough coefficients in kinetic diffusion. Learn about recent quantitative robust methods based on trajectory construction and their connections to control theory and hypocoercivity. The presentation covers recent developments by researchers including Pascucci-Polidoro, Wang-Zhang, Golse-Imbert-Mouhot-Vasseur, and others who have expanded this significant area of PDE analysis that originally solved Hilbert's 19th problem. This two-hour lecture is part of a series available on CARMIN.tv, a French video platform specializing in mathematics research content.
