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Explore a comprehensive lecture on functional inequalities in metric geometry, focusing on their role as invariants in bi-Lipschitz embeddings of finite graphs into Banach and metric spaces. Delve into various discrete functional inequalities, including nonlinear versions of type and cotype, Markov convexity, diamond convexity, and the nonlinear spectral gap inequality. Examine how these invariants lead to nonembeddability results for specific graph structures such as the Hamming cube, l∞-grids, trees, diamond graphs, and expanders. Gain insights into the intersection of functional analysis, metric geometry, and graph theory through this advanced mathematical exploration presented by Alexandros Eskenazis at the Hausdorff Center for Mathematics.
