Explore a 24-minute conference talk by Galyna Livshyts from Georgia Institute of Technology on a conjectural symmetric version of the Ehrhard inequality. Delve into the sharp inequality about Gaussian measure of Minkowski sum of sets and examine a proposed conjecture for symmetric and convex sets. Investigate the functional minimization on "k-round cylinders" and its connection to Gaussian perimeter of symmetric sets. Discover new lower estimates for this functional and understand the equality cases characterized as k-round cylinders. Learn about the equality cases in the general form of the Brascamp-Leib inequality on convex sets. Gain insights into the methods combining variational calculus with L2 estimates in this presentation from IPAM's Calculus of Variations in Probability and Geometry Workshop.