Hang Xu


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

E-mail: h9xu@ucsd.edu 



I am currently a SEW Assistant Professor in the Department of Mathematics at UC San Diego, working with Prof. Peter Ebenfelt and 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 Several Complex Variables and Complex Geometry, in particular the Bergman kernel and its asymptotic expansion.



Winter 2022: Math 142B, Introduction to Analysis II.

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), to appear in Comm. Anal. Geom., 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), to appear in Indiana Univ. Math. J., arXiv-pdf.






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