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 .

I am an assistant professor of mathematics at UCLA starting in July 2021.

Email: hongwang@math.ucla.edu

Office: Math Sciences Building, Room MS 6921.

HIM summer school: polynomial method in restriction theory:

Lecture 1-2. Lecture 3-4.

Publications and preprints

  1. The Bochner-Riesz problem: an old approach revisited, with S. Guo, C. Oh, S. Wu and R. Zhang.

  2. Improved decoupling for the parabola , with L. Guth and D. Maldague, accepted by JEMS.

3. 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.

4. Optimal Analysis of Subset-Selection Based l^p Low-Rank Approximation, with C. Dan, H. Zhang, Y. Zhou, P. Ravikumar, NeurIPS 2019.

5. 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)

6. A sharp square function estimate for the cone in $\mathbb{R}3$ with L. Guth and R. Zhang, Ann. of Math (2020).

7. Small cap decouplings with C. Demeter and L. Guth, with appendix by Roger Heath-Brown, GAFA (2020).

8. Incidence estimates for well spaced tubes with L. Guth and N. Solomon, GAFA (2019).

9. Lower bounds for estimates of the Schr\" odinger maximal function with X. Du, J. Kim and R. Zhang, Math. Res. Let. (2020)

10. On Falconer's distance set problem in the plane with L. Guth, A. Iosevich and Y. Ou, Invent. Math(2019).

11. 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)

12. A restriction estimate in $\mathbb {R}^ 3$ using brooms, accepted by Duke Math. J. (2021).

13. A cone restriction estimate using polynomial partitioning with Y. Ou, accepted by JEMS(2021).

14. On a bilinear Strichartz estimate on irrational tori and some application with C. Fan, G. Staffilani and B. Wilson, Analysis&PDE(2018).

15. Refinements of the 2-dimensional Strichartz estimate on the maximum wavepacket with L. Zhang.

16. Decoupling and near-optimal restriction estimates for Cantor sets with I. Laba, IMRN(2017).

17. Exposition of Elekes Szabo paper.

18. Bounds of incidences between points and algebraic curves with B. Yang and R. Zhang.