AI, Data Science & Cloud Certificates from Google, IBM & Meta — 40% Off
One plan covers every Professional Certificate on Coursera. 40% off Coursera Plus Annual.
Unlock All Certificates
Listen to the second part of the Zygmund Calderón Lectures in Analysis (2025) series featuring MIT's David Jerison discussing "How Curved are Level Sets of Solutions to Elliptic PDE?" This audio-only lecture explores new geometry of level sets of semilinear elliptic equations (δ(u) = f(u)), drawing inspiration from Hamilton and Perelman's work on mean curvature flow and Ricci flow. Discover potential applications to level sets of eigenfunctions, beginning with harmonic functions. Learn about two fundamental tools of algebraic and differential geometry: Jacobi functions and the Levi-Civita affine connection. Note that due to technical difficulties, only the audio was captured for this one-hour lecture presented by the University of Chicago Department of Mathematics.
