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Explore vector-valued concentration inequalities for the uniform measure on the symmetric group in this 52-minute lecture by Mira Gordin from the Hausdorff Center for Mathematics. Delve into the novel inequality presented and its implications for embedding distortions of the symmetric group into Banach spaces, a topic relevant to metric geometry and algorithmic applications. Learn how this work builds upon previous research by Ivanisvili, van Handel, and Volberg on vector-valued inequalities in the discrete hypercube, addressing Enflo's question in Banach space metric theory. Gain insights into the differences between well-understood real-valued function concentration and the less explored vector-valued function concentration phenomena. Discover the connections between probabilistic tools, theoretical concepts, and practical applications in this advanced mathematical discussion based on joint work with Ramon van Handel.
