Publications and Preprints:

1. Strichartz estimates for the Schrödinger equation on Zoll manifolds, preprint (With Christopher D. Sogge)

2. Lossless Strichartz and spectral projection estimates on unbounded manifold, preprint (With Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang)

3. Restriction of Schrödinger eigenfunctions to submanifolds, preprint (With Xing Wang and Cheng Zhang)

4. Curvature and sharp growth rates of log-quasimodes on compact manifolds, Invent. math. (2025). https://doi.org/10.1007/s00222-025-01315-2 (With Christopher D. Sogge)

5. Global uniform in N estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime, American Journal of Mathematics, to appear.

6. Improved spectral projection estimates, J. Eur. Math. Soc. (2024), DOI 10.4171/JEMS/1571.(With Matthew D. Blair  and Christopher D. Sogge)

7. On Strichartz estimates for many-body Schrödinger equation in the periodic setting, Forum Mathematicum, https://doi.org/10.1515/forum-2024-0105. (With  Xueying Yu, Zehua Zhao and Jiqiang Zheng).

8. Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature, Journal of Spectral Theory, to appear (With Christopher D. Sogge)

9. Quasimode concentration on compact space forms, preprint (With Christopher D. Sogge)

10. Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds,  Journal of Functional Analysis, Volume 287, Issue 10, 15 November 2024 (With Matthew D. Blair  and Christopher D. Sogge)

11. Sharp Lp estimates and size of nodal sets for generalized Steklov eigenfunctions, preprint (With Yannick Sire, Xing Wang and  Cheng Zhang) 

12. Heat kernel estimate in a conical singular space, J. Geom. Anal, Volume 33, article number 284, (2023) (with Junyong Zhang)

13. Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates, "From Classical Analysis to Analysis on Fractals - The Robert Strichartz Memorial Volume", Springer, 2023 (with Christopher D. Sogge and Michael Taylor)

14. Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori, Communications in Mathematical Physics, Volume 401, pages 1063–1125, (2023) (with Cheng Zhang)

15. Pointwise Weyl laws of Schrödinger operators with singular potentials, Advances in Mathematics,  Volume 410, Part A, 3 December 2022 (with Cheng Zhang)

16. Uniform Sobolev estimates in R^n involving singular potentials, J. Geom. Anal., 32, Article number: 68 (2022). (With Christopher D. Sogge) 

17. Quasimode and Strichartz estimates for time-dependent Schrödinger equations with singular potentials, Math. Research Letters, Volume 29 (2022) Number 3. (With Christopher D. Sogge)

18. Uniform Sobolev Estimates on compact manifolds involving singular potentials, Rev. Mat. Iberoam., Vol.37/No.1/pp.1-414/2021.. (With Matthew D. Blair, Christopher D. Sogge and Yannick Sire) 

19. Weyl formulae for Schrödinger operators with critically singular potentials, Comm. Partial Differential Equations, Volume 46, 2021 - Issue 11. (With Christopher D. Sogge) 

20. Spectral cluster estimates for Schrödinger operators of relativistic type, Journal des Mathématiques Pures et Appliquées, Volume 155, November 2021, Pages 32-61. (With Yannick Sire and Cheng Zhang)

21. Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain, Advances in Mathematics, Volume 392, 3 December 2021, 108032. (With Yannick Sire and Cheng Zhang)

22. Restriction of toral eigenfunctions to totally geodesic submanifolds, Analysis & PDE, Vol. 14 (2021), No. 3, 861–880. (With Cheng Zhang)

My research is supported in part by the National Science Foundation and the Simons Foundation.