Hong Wang（王虹）
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 we say about this function? How to decompose this function into pieces in a meaningful way (which is related to the decoupling theory)? It turns out that such problems are also related to the Falconer distance problem and incidence geometry and I'm interested in these connections.
2019-2021, I was a postdoc member at the IAS ; 2021-2023, I was an assistant professor at UCLA.
I am an associate professor of mathematics at NYU Courant..
Email: hw3639@nyu.edu
Office: WWH 716
SLMath Hot topic workshop: Interactions between Harmonic analysis, homogeneous dynamics, and number theory. March 3-7, 2025. Co-organize with Dubi Kelmer and Amir Mohammadi.
Publications and preprints
The Assouad dimension of Kakeya sets in $\mathbb{R}^3$ with J. Zahl.
How much can heavy slices cover? with D. Dabrowski and T. Orponen., accepted by JLMS.
Furstenberg sets estimate in the plane , with K. Ren.
Some sharp inequalities of Mizohata--Takeuchi-type , with A. Carbery and M. Iliopoulou, accepted by Revisita.
Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem , with P. Shmerkin, accepted by APDE.
A restricted projection problem for fractal sets in $\mathbb{R}^n$ , with S. Gan and S. Guo, accepted by Cambridge Journal of Mathematics.
Sticky Kakeya sets and the sticky Kakeya conjecture , with J. Zahl.
A dichotomy for H\"{o}rmander type oscillatory integral operators, with S. Guo and R. Zhang.
An improved restriction estimate in $\mathbb{R}^3$, with S. Wu.
Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem , with T. Orponen and P. Shmerkin, accepted by GAFA.
On restricted projections to planes in $\mathbb{R}^3$, with S. Gan, S. Guo, L. Guth, T. Harris, D. Maldague, accepted by Amer. J. M.
On the distance sets spanned by sets of dimension d/2 in $\mathbb{R}^d$ with P. Shmerkin.
The Bochner-Riesz problem: an old approach revisited, with S. Guo, C. Oh, S. Wu and R. Zhang, accepted by Peking Math Journal.
Improved decoupling for the parabola , with L. Guth and D. Maldague, accepted by JEMS.
An improved result for Falconer's distance set problem in even dimensions, with X. Du, A. Iosevich, Y. Ou, and R. Zhang, accepted by Math. Annalen.
Optimal Analysis of Subset-Selection Based l^p Low-Rank Approximation, with C. Dan, H. Zhang, Y. Zhou, P. Ravikumar, NeurIPS 2019.
2D-Defocusing Nonlinear Schrodinger equation with random data on irrational tori with C. Fan, Y. Ou and G. Staffilani, Stoch. Partial Differ. Equ. Anal. Comput. (2021)
A sharp square function estimate for the cone in $\mathbb{R}3$ with L. Guth and R. Zhang, Ann. of Math (2020).
Small cap decouplings with C. Demeter and L. Guth, with appendix by Roger Heath-Brown, GAFA (2020).
Incidence estimates for well spaced tubes with L. Guth and N. Solomon, GAFA (2019).
Lower bounds for estimates of the Schr\" odinger maximal function with X. Du, J. Kim and R. Zhang, Math. Res. Let. (2020)
On Falconer's distance set problem in the plane with L. Guth, A. Iosevich and Y. Ou, Invent. Math(2019).
Weighted restriction estimates and application to Falconer distance set problem with X. Du, L. Guth, Y. Ou, B. Wilson and R. Zhang, Amer. J. Math. (2021)
A restriction estimate in $\mathbb {R}^ 3$ using brooms, Duke Math. J. (2022).
A cone restriction estimate using polynomial partitioning with Y. Ou, JEMS(2022).
On a bilinear Strichartz estimate on irrational tori and some application with C. Fan, G. Staffilani and B. Wilson, Analysis&PDE(2018).
Refinements of the 2-dimensional Strichartz estimate on the maximum wavepacket with L. Zhang.
Decoupling and near-optimal restriction estimates for Cantor sets with I. Laba, IMRN(2017).
Bounds of incidences between points and algebraic curves with B. Yang and R. Zhang.