Quantitative Stability in Geometric and Functional Inequalities II

Geometric and functional inequalities are fundamental in various mathematical areas, such as the calculus of variations, partial differential equations, and geometry. Classic examples encompass the isoperimetric inequality, Sobolev inequalities, and the Brunn-Minkowski inequality, to name a few. A natural question in this context is the stability of these inequalities: if a function or set nearly achieves equality, how close is it to the actual minimizer? These lectures will introduce this beautiful topic and discuss some recent advancements.