Hong Wang 王虹

I am a mathematician working in harmonic analysis and geometric measure theory. I am Silver Professor of Mathematics at NYU Courant and a permanent professor at IHES. My research asks how waves, lines, tubes, distances, and fractal sets constrain one another across different scales.

我是一名研究调和分析与几何测度论的数学家，现任纽约大学 Courant 数学科学研究所 Silver Professor，并任法国高等科学研究所（IHES）数学终身教授。我的研究关注波、直线、细管、距离与分形集合如何在不同尺度上彼此制约。

My work connects restriction theory, local smoothing, projection and distance problems, Furstenberg sets, and the Kakeya problem. In joint work with Joshua Zahl, we proved the three-dimensional Kakeya set conjecture. I see that result as one point in a longer research path: many central questions in restriction theory and higher-dimensional Kakeya remain open.

我的工作连接限制性理论、局部光滑、投影与距离问题、Furstenberg 集以及 Kakeya 问题。我与 Joshua Zahl 合作证明了三维 Kakeya 集合猜想。对我而言，这一结果是更长研究路径中的一个节点：限制性理论以及更高维 Kakeya 中仍有许多核心问题尚未解决。

When I work on a difficult problem, I try to simplify it, test examples, learn from failed approaches, and reassess what the evidence is saying. Collaboration and conversation are essential parts of that process. I try to remain honest about progress—neither too optimistic nor too pessimistic—and then continue working.

面对困难问题时，我会尝试把它简化、检验具体例子、从失败的方法中学习，并重新判断现有证据究竟说明了什么。合作与讨论是这个过程的重要部分。我会尽量诚实地看待进展——既不过分乐观，也不过分悲观——然后继续推进。