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Explore stochastic geometry of s-concave functions in this 29-minute lecture by Peter Pivovarov from the Hausdorff Center for Mathematics. Delve into the concept of "local" stochastic isoperimetry and its role in various functional inequalities. Discover a new perspective through the introduction of shadow systems for s-concave functions. The talk draws from joint research with J. Rebollo Bueno, offering insights into the intersection of probability theory, geometry, and functional analysis.