The David-Semmes Problem, Rectifiability, and Harmonic Measure - ICBS 2024

Explore the solution to the David-Semmes problem in codimension one and its implications for harmonic measure in this 47-minute lecture. Delve into the intricacies of the n-dimensional Riesz transform and its connection to n-rectifiability. Learn about the groundbreaking work by Nazarov, Tolsa, and Volberg from 2014, and discover how their findings played a crucial role in solving one-phase and two-phase problems for harmonic measure proposed by Bishop in the early 1990s. Gain insights into the mathematical concepts of rectifiability, harmonic measure, and their interplay in solving complex geometric problems.