Furstenberg Sets Estimates with Application to Restriction Theory

Explore advanced mathematical concepts in this conference talk examining Furstenberg sets and their applications to Fourier restriction theory. Learn about Kakeya sets as compact subsets of $\mathbb{R}^n$ containing unit line segments in every direction, and discover the generalization to $s$-Furstenberg sets where intersections with unit line segments maintain specific Hausdorff dimension properties. Understand how dimension estimates for these sets emerge naturally through wave packet decompositions in Fourier restriction theory, and examine why considering $s$-dimensional subsets of line segments becomes mathematically relevant when waves concentrate on sparser tube subsets. Gain insights into current research developments through discussion of collaborative work with Shukun Wu and ongoing investigations with Dima Zakharov, presented by a researcher from both IHES and NYU.