Recorded 07 February 2022. Grigorios Paouris of Texas A&M University - College Station presents Empirical Isoperimetric Inequalities outside convexity at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Several classical isoperimetric inequalities for convex sets have been extended to "empirical ones" in the last decade. In the empirical setting, a geometric quantity of a random convex set generated by samples drawn from an arbitrary distribution in the n-dimensional space is minimized (maximized) when the samples are drawn uniformly from the Euclidean ball. This talk will report some new empirical isoperimetric inequalities involving non-convex sets