Fall 2021: Math 120A, Applied Complex analysis I.
Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann-Fock Model (with Hamid Hezari, Casey Kelleher and Shoo Seto). Journal of Geometric Analysis (2016) 26: 2602,
2. On instability of the Nikodym maximal function bounds over Riemannian manifolds, (with Christopher Sogge and Yakun Xi), Journal of Geometric Analysis (2018) 28: 2886,
Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kahler potentials (with Hamid Hezari and Zhiqin Lu), IMRN,
4. Quantitative upper bounds for Bergman Kernels associated to smooth Kahler potentials (with Hamid Hezari), to appear in Math. Research Letters,
5. Analysis of The Laplacian on the moduli space of polarized Calabi-Yau manifolds (with Zhiqin Lu), to appear in Hopkins-Maryland Complex Geometry Seminar proceedings, Contemp. Math., Amer. Math. Soc.
6. Asymptotic properties of Bergman kernels for potentials with Gevrey regularity,
7. Upper bounds for eigenvalues of conformal Laplacian on closed Riemannian manifolds (with Yannick Sire), to appear in Commun. Contemp. Math., arXiv-pdf.
8. On a property of Bergman kernels when the Kahler potential is analytic (with Hamid Hezari), to appear in Pacific J. Math., arXiv-pdf.
9. Algebraicity of the Bergman kernel (with Peter Ebenfelt and Ming Xiao), submitted, arXiv-pdf.
10. The Dirichlet principle for the complex k-Hessian functional (with Yi Wang), submitted, arXiv-pdf.
11. On the classification of normal Stein spaces and finite ball quotients with Bergman-Einstein metrics (with Peter Ebenfelt and Ming Xiao), IMRN, arXiv-pdf.
12. Algebraic degree of the Bergman kernel (with Peter Ebenfelt and Ming Xiao), in preprint.