GÖRAN GUSTAFSSON Lectures in Mathematics May 24–26, 2021 KTH, Stockholm
Alessio Figalli
QUANTITATIVE STABILITY IN GEOMETRIC AND FUNCTIONAL INEQUALITIES 
Abstract Geometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The issue of the sharpness of a constant, as well as the characterization of minimizers, is a classical and important question. More recently, there has been a growing interest in studying the stability of such inequalities. The basic question one wants to address is the following: Suppose we are given a functional inequality for which minimizers are known. Can we quantitatively show that if a function “almost attains the equality,” then it is close to one of the minimizers? In this series of lectures, I will first give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev, isoperimetric, and Brunn–Minkowski inequalities. Lectures Lecture 1:
Monday, May 24, 3.00–4.00 pm
Lecture 2:
Tuesday, May 25, 2.00–3.00 pm
Lecture 3:
Wednesday, May 26, 2.00–3.00 pm
