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The course covers fundamental properties of solutions to elliptic partial differential equations and associated boundary value problems, and introduces basic related tools of modern harmonic analysis and geometric measure theory.

In this reading course, we will explore harmonic measure and its connections to harmonic analysis, rough geometry, and probability. If time permits, we will also explore analogues of harmonic measure to domains with higher co-dimensional boundaries.

This course aims to provide an overview of the mathematics of turbulence. The first half will be devoted to the theory of fully developed turbulence a la Kolmogorov and Onsager, the Richardson cascade, and intermittency. The second will involve more advanced topics such as anomalous dissipation and fractal structures. We also touch on some elements of GMT and calculus of variations.