Tuesday 19 November 2024, 16:00 - 17:00 in HG03.085
Max Goering (Jyväskylä)
Tangents and rectifiability in a rough Riemannian setting
One of the core goals of geometric measure theory is to understand when a measure is rectifiable. Rectifiable measures are a measure-theoretic generalization of (Lipschitz) manifolds. There are two prevailing methods to study rectifiability: multi-scale analysis and blow-up analysis. In this talk, I will introduce \(\Lambda\)-tangents, a generalization of Preiss' tangent measures that I developed with collaborators E. Casey, T. Toro, and B. Wilson. After a gentle introduction to the tools and review of the history, the talk will primarily focus on the relationship between the analytic behavior of singular integral operators and the geometry of measures, as well as an application to PDEs.