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Friday, November 12, 2021

**Abstract:** Abstract: This talk introduces functional and geometric inequalities, opening with a discussion about what they are and key questions that frame their study. We prove the Polya-Szego inequality and then use it to establish the classical Faber-Krahn inequality, which states that balls minimize the first eigenvalue of the Dirichlet Laplacian among all sets of the same volume. We conclude by outlining what a more general Faber-Krahn inequality looks like and how one might go about deriving it. This talk is based on a paper by Brasco and De Phillips (2016).