Recorded 08 February 2022. Alessio Figalli of ETH Zurich presents "Quantitative Stability in Geometric and Functional Inequalities" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Geometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. Proving the validity of such inequalities, and understanding the structure of minimizers, is a classical and important question. In this talk, I will give an overview of this beautiful topic and discuss some recent results.