Technically, my research mainly focuses on microlocal analysis. In terms of topics, I am interested in wave and dispersive equations, and mathematical physics.
Research papers (newest first):
Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds (with Junyong Zhang), preprint.
The essential self-adjointness of the wave operator on radiative spacetimes (with Mikhail Molodyk, Ethan Sussman), preprint.
Strichartz estimates for the Schrödinger equation in high dimensional critical electromagnetic fields (with Junyong Zhang), preprint.
The final state problem for the nonlinear Schrodinger equation in dimensions 1, 2 and 3 (with Andrew Hassell), preprint.
Pointwise dispersive estimates for Schrodinger and wave equations on conical singular spaces (with Junyong Zhang), preprint
Interior analysis, stretched technique and bubbling geometries (with Hai Lin), published in Annals of Physics.
The tensorial X-ray transform on asymptotically conic spaces (with András Vasy), published in Inverse Problems and Imaging.
Propagation of Singularity with Normally Hyperbolic Trapping , published in Annales Henri Poincaré.
2D Inverse Problems with a Foliation Condition , preprint.
Dimensional Reweighting Graph Convolutional Networks (with Xu Zou et al.), preprint.
Calabi–Yau generalized complete intersections and aspects of cohomology of sheaves (with Hai Lin), published in Journal of Mathematical Physics.
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Notes/Expository papers/other fun stuffs:
Propagation of Singularities on Kerr(-de Sitter) Spacetimes , to appear in the 2023 volume of the book series MATRIX Annals. This is an expository version of the Propagation of Singularity with Normally Hyperbolic Trapping above.
The topological pressure of trapped sets in Kerr-(de Sitter) spacetimes
Regularity of distributions with zero measure support
Automorphisms of the algebra of smooth functions on compact manifolds (I found later that this is already contained in [Lemma2, Duistermaat-Singer 1976]. )