Research

Publications and Preprints:

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

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)

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)

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

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) 

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

Uniform Sobolev estimates in $\mathbb{R}_n$ involving singular potentials, J. Geom. Anal., 32, Article number: 68 (2022). (With Christopher D. Sogge) 

Pointwise Weyl laws of Schr\"odinger operators with singular potentials, Advances in Mathematics,  Volume 410, Part A, 3 December 2022 (with Cheng Zhang)

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

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)

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

Global uniform in N estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime, preprint

Improved spectral projection estimates, Journal of the European Mathematical Society,  to appear .(With Matthew D. Blair  and Christopher D. Sogge)

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

Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds, preprint (With Matthew D. Blair  and Christopher D. Sogge)

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

Curvature and sharp growth rates of log-quasimodes on compact manifolds, preprint (With Christopher D. Sogge)