Explore a lecture on tight convexity inequalities for symmetric convex sets, delivered by Galyna Livshyts at the Hausdorff Center for Mathematics. Delve into a conjectured inequality strengthening the Ehrhard inequality for symmetric convex sets in the case of standard Gaussian measure. Examine its connections to isoperimetric problems and the Dirichlet-Poincare inequality, with round k-cylinders as optimizers. Investigate progress using L2 methods, energy minimization, and related estimates. Learn about equality case characterization based on quantitative stability in energy minimization and the Brascamp-Lieb inequality. Discover new inequalities for other measures and gain insights into topics such as the Minkowski inequality, Gaussian symmetric cases, and correlation inequalities.