Teaching
Fall 2026
Functional Inequalities: From Analysis to Probability
21-317 Topics in Analysis · Undergraduate
This course introduces several central functional inequalities in modern analysis and probability, including Poincaré, Sobolev, logarithmic Sobolev, and isoperimetric inequalities, together with selected applications.
Topics include spectral gap and variance decay, concentration of measure, entropy methods, and convergence to equilibrium for Markov processes. Examples are drawn from Euclidean, Gaussian, and discrete settings, with selected applications to partial differential equations, mathematical physics, statistics, and machine learning.
The course is organized substantially around student presentations of foundational and current research papers, alongside an expository writing project.
Official course description and prerequisites →
This course is supported by the National Science Foundation through grant DMS-2441170.