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Explore the inverse isoperimetric problem in graph theory through this comprehensive lecture. Delve into the structure of vertex subsets with minimal edge connections to their complements. Examine the Fourier-Entropy-Influence conjecture, a key problem in the Hamming cube's inverse isoperimetric landscape, and its applications to PAC learning and other fields. Gain insights into recent advancements towards resolving this conjecture and related inverse isoperimetric inequalities. The talk draws from collaborative research with Evra, Kelman, Kindler, Keevash, Minzer, and Safra, offering a deep dive into this fascinating area of mathematics over the course of 1 hour and 14 minutes.
