Measures with L2-Bounded Riesz Transform and the Painlevé Problem for Lipschitz Harmonic Functions

Explore the intricacies of L2-bounded Riesz transform measures and the Painlevé problem for Lipschitz harmonic functions in this 55-minute lecture by Xavier Tolsa from Universitat Autonoma de Barcelona. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute, delve into key concepts such as uniform rectifiability, curvature of measures, and removability. Examine the importance of curvature, uncover significant theorems and their consequences, and learn about the Brazilian Theorem and the Knife Approach. Gain insights into this complex mathematical topic through a structured presentation that covers definitions, problems, proofs, and concludes with a final theorem and Q&A session.

Introduction
Definitions
Problem
Uniform Rectifiability
The curvature of measures
Why is curvature important
Theorem
Consequences
Removability
Proof
The Brazilian Theorem
The Knife Approach
Final Theorem
Questions