Hang Xu


APM 6305
Department of Mathematics
University of California, San Diego 
9500 Gilman Dr, La Jolla, CA 92093   




I am currently a SEW Assistant Professor in the Department of Mathematics at UC San Diego, working with Prof. Ming Xiao. Before that, I was a J. J. Sylvester Assistant Professor in the Department of Mathematics at Johns Hopkins University, working with Prof. Bernard Shiffman. I received my PhD in 2016 from Department of Mathematics from University of California, Irvine, under Prof. Zhiqin Lu.


My research field is Kahler geometry. I am mainly interested in Bergman kernel and its asymptotic expansion. 



Fall 2021: Math 18, Linear Algebra.

Fall 2021: Math 120A, Applied Complex analysis I.


Research Publications

1.      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, arXiv-pdf.

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, arXiv-pdf.

3.      Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kahler potentials (with Hamid Hezari and Zhiqin Lu), IMRN, arXiv-pdf.

4.      Quantitative upper bounds for Bergman Kernels associated to smooth Kahler potentials (with Hamid Hezari), to appear in Math. Research Letters, arXiv-pdf.  

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, arXiv-pdf.

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.







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