Research
Papers:
Kakeya sets from lines in SL_2 (with Nets Katz and Joshua Zahl).
An improved restriction estimate in R^3 (with Hong Wang).
Square function estimates for conical regions (with Shengwen Gan), To appear in Indiana Univ. Math. J. (2022).
Heat kernel estimates for non-local operator with critical killing potential (with Renming Song and Peixue Wu).
A note on local smoothing estimates for fractional Schrödinger equations (with Shengwen Gan and Changkeun Oh), J. Funct. Anal. 283 (2022), no. 5, Paper No. 109558.
New bounds for Stein's square functions in higher dimensions (with Shengwen Gan and Changkeun Oh).
New bounds for Stein’s square function in R3 (with Shengwen Gan and Yifan Jing).
The Bochner-Riesz problem: an old approach revisited (with Shaoming Guo, Changkeun Oh, Hong Wang, and Ruixiang Zhang).
A note on the largest sum-free sets of integers. (with Yifan Jing).
On the Bochner-Riesz operator in R3. To appear in J. Anal. Math (2022).
On the refined Strichartz estimates and maximal extension operator. J. Fourier Anal. Appl. 27 (2021), no. 3, Article No. 48.
The largest (k,ℓ)-sum-free subsets. (with Yifan Jing).Trans. Amer. Math. Soc. 374 (2021), no. 7, 5163–5189.
New estimates of maximal Bochner-Riesz operator in the plane. (with Xiaochun Li), Math. Ann. 378 (2020), no. 3-4, 873–890.
Service:
Co-organizer (with David Conlon and Nets H. Katz and Tom Hutchcroft): Discrete Analysis seminar at Caltech, 2021-present.
Co-organizer (with Chuanwei Gao and Yujia Zhai and Jiqiang Zheng): Workshop on Harmonic Analysis, Nov 2021.
Grant:
AMS-Simons Travel Grants