About
I am a Hedrick Assistant Adjunct Professor in the Department of Mathematics, at UCLA, mentored by Michael Hitrik. I received my Ph.D. at Berkeley under the supervision of Maciej Zworski.
Here is my CV. I am currently on the job market for tenure track positions.
I am interested in Scattering Theory, Microlocal Analysis, and Partial Differential Equations.
E-mail: haorenxiong at math dot ucla dot edu
Papers and Preprints
Boundary spectral estimates for semiclassical Gevrey operators, submitted, arXiv: 2408.09098.
Asymptotic expansions for semilinear waves on asymptotically flat spacetimes, (with Shi-Zhuo Looi), submitted, arXiv: 2407.08997.
Semiclassical asymptotics for Bergman projections with Gevrey weights, (with Hang Xu), submitted, arXiv: 2403.14157.
Boundedness of metaplectic Toeplitz operators and Weyl symbols, J. Funct. Anal. 286 (2024), 110294. (arXiv: 2305.03948).
Generic simplicity of resonances in obstacle scattering, Trans. Amer. Math. Soc. 376 (2023), 4301-4319.
Resonances as viscosity limits for black box perturbations, Annales Henri Poincaré 23 (2022), 675-705.
Resonances as viscosity limits for exponentially decaying potentials, Journal of Mathematical Physics 62 (2021), 022101.
Complex Higgs Oscillators, arXiv: 2109.09303.
Resonances as viscosity limits for exterior dilation analytic potentials, arXiv: 2002.12490.
Talks
Harmonic Analysis and Differential Equations Student Seminar, UC Berkeley: The method of complex scaling [Aug 2019]
Harmonic Analysis and Differential Equations Student Seminar, UC Berkeley: Complex absorbing potential method for calculating scattering resonances (exponentially decaying potentials) [Feb 2022]
QMATH 15, Spectral Theory session, UC Davis: Complex absorbing potential method for calculating scattering resonances (black box scattering) [Sep 2022]
Analysis and PDE Seminar, UC Berkeley: Toeplitz operators, semiclassical asymptotics for Bergman projections [Feb 2024]
Harmonic Analysis Seminar, UC Irvine: Semiclassical asymptotics for Bergman projections [Oct 2024]
Analysis and PDE Seminar, UCLA: Semiclassical asymptotics for Bergman projections [Nov 2024]
Real Analysis Seminar, UCSD: Semiclassical asymptotics for Bergman projections [Feb 2025]