Variational Proofs of Isoperimetric Inequalities

Explore a comprehensive lecture on variational proofs of isoperimetric inequalities presented by Steven Heilman from the University of Southern California. Delve into a survey of variational proofs for Euclidean and Gaussian isoperimetric inequalities, understanding their benefit in identifying local minima. Discover two methods of generalizing these inequalities: replacing one set with multiple sets and substituting surface area with heat content (known as noise stability in the Gaussian setting). Gain insights into open problems in the field and learn about the collaborative work with Alex Tarter. This 31-minute talk, recorded on February 11, 2022, is part of the Calculus of Variations in Probability and Geometry Workshop organized by the Institute for Pure & Applied Mathematics (IPAM).