Hong Wang - Furstenberg Sets Estimates with Application to Restriction Theory @IhesFr

Uploaded January 2026 | Updated September 2026, 2 weeks ago

A Kakeya set is a compact subset of $\mathbb{R}^n$ containing a unit line segment in every direction. More generally, for $0 \lt s \leq 1$, an $s$-Furstenberg set is a subset $E \subset \mathbb{R}^n$ such that for every direction there is a unit line segment whose intersection with $E$ has Hausdorff dimension at least $s$. Furstenberg set problems ask for lower bounds on ${\rm dim}_H(E)$ in terms of $s$ and $n$.
In this talk I will discuss how such dimension estimates arise naturally in Fourier restriction theory via wave packet decompositions. From this perspective it is natural to consider s-dimensional subsets of line segments, rather than whole segments, because waves may concentrate on sparser subsets of tubes.
This is based on joint work with Shukun Wu and joint work in progress with Dima Zakharov.

Hong Wang (IHES & NYU)

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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.

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$Hong Wang - Furstenberg Sets Estimates with Application to Restriction Theory A Kakeya set is a compact subset of $mathbb{R}^n$ containing a unit line segment in every direction. More generally, for $0 lt s leq 1$, an $s$-Furstenberg set is a subset $E subset mathbb{R}^n$ such that for every direction there is a unit line segment whose intersection with $E$ has Hausdorff dimension at least $s$. Furstenberg set problems ask for lower bounds on ${rm dim}_H(E)$ in terms of $s$ and $n$. In this talk I will discuss how such dimension estimates arise naturally in Fourier restriction theory via wave packet decompositions. From this perspective it is natural to consider s-dimensional subsets of line segments, rather than whole segments, because waves may concentrate on sparser subsets of tubes. This is based on joint work with Shukun Wu and joint work in progress with Dima Zakharov. Hong Wang (IHES & NYU) Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.$

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