Title: Exploring Stability in Geometric and Functional Inequalities

Speaker: Alessio Figalli (ETH)

Date, Time, Location: Wednesday, November 13th @4:30PM in Math Hall 520

Abstract: In the realms of analysis and geometry, geometric and functional inequalities are of paramount significance, influencing a variety of problems. Traditionally, the focus has been on determining precise constants and identifying minimizers. More recently, there has been a growing interest in investigating the stability of these inequalities. The central question we aim to explore is: “If a function nearly achieves equality in a known functional inequality, can we demonstrate, in a quantitative way, its proximity to a minimizer?” In this colloquium, I will first overview this topic and discuss some recent results.

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