Bounds on the Hausdorff Measure of Zero Sets of Steklov Eigenfunctions

Explore the intricacies of Steklov eigenfunctions and their zero sets in this 31-minute lecture by Stefano Decio from the Hausdorff Center for Mathematics. Delve into recent findings on upper bounds for the Hausdorff measure of zero sets, drawing comparisons with the more extensively studied Laplace eigenfunctions. Follow the progression from introductory concepts to advanced topics, including the problem statement, examples, conjectures, and breakthrough discoveries. Examine key elements such as boundary conditions, doubling indices, and the Zoo theorem. Gain insights into rescaling techniques and the Hyperplane lemma as they relate to this fascinating area of mathematical research.

Introduction
The problem
The zero set
First example
Second example
conjecture
upper bounds
a promise
the big conjecture
the big breakthrough
a trick
boundary condition
Doubling indices
Zoo theorem
Rescale
Hyperplane lemma