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Explore key geometric problems in analysis that have been successfully approached using multilinear methods over the past 15 years in this one-hour lecture by Tony Carbery from the University of Edinburgh. Gain insights into how these problems, originating in harmonic analysis, have been tackled using ideas from nonlinear analysis, functional analysis, and discrete analysis. Delve into the intersection of geometry and analysis, understanding how diverse analytical techniques contribute to solving complex mathematical challenges.