This is a blog version of a talk I recently gave at the IPAM workshop on “The Kakeya Problem, Restriction Problem, and Sum-product Theory”. Note: the discussion here will be highly non-…| What's new
Hello! I'm Hong Wang. I did my PhD with Prof. Larry Guth at MIT in 2019. I'm interested in Fourier analysis and related problems. For example, if we know that the Fourier transform of a function is supported on some curved objects, a sphere, or some "curved" collection of discrete points, what can| sites.google.com
The most up-to-date version of my webpage can be found here.| personal.math.ubc.ca
We study sets of $δ$ tubes in $\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almost maximal volume. As a consequence, we prove that every Kakeya set in $\mathbb{R}^3$ has Minkowski and Hausdorff dimension 3.| arXiv.org
A Kakeya set is a compact subset of $\mathbb{R}^n$ that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have Hausdorff and Minkowski dimension $n$. There is a special class of Kakeya sets, called sticky Kakeya sets. Sticky Kakeya sets exhibit an approximate multi-scale self-similarity, and sets of this type played an important role in Katz, Łaba, and Tao's groundbreaking 1999 work on the Kakeya problem. We propose a special case of ...| arXiv.org
There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set con…| What's new
