Functional Inequalities: From Analysis to Probability

The Fall 2026 course website for 21-317 Topics in Analysis at Carnegie Mellon University.

21-317 Topics in Analysis · Fall 2026

Functional Inequalities

From Analysis to Probability

A course on the inequalities that connect geometry, probability, and dynamics—and on how to read, explain, and write research-level mathematics.

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Welcome to 21-317

This site is the public home for the syllabus, weekly schedule, course notes and readings, and dated announcements.

The course develops Poincaré, Sobolev, logarithmic Sobolev, and isoperimetric inequalities together with selected applications. We will move among Euclidean, Gaussian, and discrete settings, emphasizing spectral gaps, concentration of measure, entropy methods, and convergence to equilibrium for Markov processes.

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This course is supported by the National Science Foundation through grant DMS-2441170. See the official CMU course description and prerequisites.

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