Several Complex Variables, Complex Geometry, CR Geometry, and Partial Differential Equations.
2009 - May 2015, Ph.D. in Mathematics, Rutgers
2005 - 2009, B.S. in Mathematics, Univ. of Science and Technology of China, Hefei, China.
July 2021-Present Associate Professor, Department of Mathematics, UCSD
July 2017-June 2021 Assistant Professor, Department of Mathematics, UCSD
August 2015-June 2017 J. L. Doob Assistant Professor, Department of Mathematics, UIUC
Publications and submitted papers:
On the smooth version of the reflection principle for mappings between CR manifolds, (joint with Shiferaw Berhanu), Amer. J. Math. 137 (2015), no.5, 1365-1400.
Nonembeddability into a fixed sphere for a family of compact real algebraic hypersurface, (joint with Xiaojun Huang and Xiaoshan Li),
Int. Math. Res. Not.(IMRN). 16 (2015), 7382-7393. [DOI: 10.1093/imrn/rnu167].
On the regularity of CR mappings between CR manifolds of hypersurface type, (joint with Shiferaw Berhanu), Trans. Amer. Math. Soc. 369 (2017), no.9 6073-6086. [PDF].
Symmetries in CR complexity theory, (joint with John D'Angelo), Adv. Math. 313 (2017), 590-627.
Proper holomorphic maps from the unit disk to some unit balls. (joint with John D'Angelo, Zhenghui Huo),
Proc. Amer. Math. Soc. 145 (2017), no.6, 2649-2660 [PDF].
On the embeddability of real hypersurfaces into hyperquadrics, (joint with Ilya Kossovskiy),
Adv. Math., 331 (2018), 239-267. arxiv: 1509.01962. [PDF].
Holomorphic maps from the complex unit ball to type IV classical domains, (joint with Yuan Yuan),
Journal de Math\'ematiques Pures et Appliqu\'ees , 133 (2020), 139-166. [PDF].
Complexity of holomorphic maps from the complex unit ball to classical domains, (joint with Yuan Yuan),
Asian J. Math. , 22 (2018), 729-760. (Special issue dedicated to Professor Ngaiming Mok) [PDF].
Volume-preserving maps between Hermitian symmetric spaces of compact type, (joint with Hanlong Fang and Xiaojun Huang),
Advances in Mathematics , 360 (2020), 106885. Here is an expanded note for the submitted version[PDF].
Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundary
(joint with Xiaojun Huang), Crelle's Journal , doi.org/10.1515/crelle-2020-0012.
Regularity of CR-mappings of codimension one into Levi-degenerate hypersurfaces,
(joint with Ilya Kossovskiy and Bernhard Lamel), Comm. Anal. Geom., 29 (2021), 151-181.
Chern-Moser-Weyl tensor and embeddings into hyperquadrics, (joint with Xiaojun Huang),
Harmonic Analysis, partial differential equations , 79-95, Appl. Numer. Harmon. Anal., Birkh\"auser/Springer, Cham, 2017 [PDF].
Holomorphic isometries between products of complex unit balls, (joint with Shan-Tai Chan and Yuan Yuan),
Intern. Math. J. , 28 (2017), no.9, 1740010, 22 pp.
Symmetries and regularity for holomorphic maps between balls, (joint with John D'Angelo),
Math. Res. Lett., 25 (2018), 1389-1404. arxiv: 1711.06539.
Regularity of mappings into classical domains, Math. Annalen , doi.org/10.1007/s00208-019-01911-7.
A CR embedding problem for an algebraic Levi non-degenerate hypersurface into a hyperquadric,
(joint with Xiaojun Huang), Geometric Comlex Analysis, (Special issue dedicatec to Professor Kang-Tae Kim),
pp 185-198, Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore.
A uniformization theorem for Stein spaces, (joint with Xiaojun Huang), Complex Analysis and its Synergies ,
(2020), 6:6, doi.org/10.1007/s40627-020-00044-x.
Boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces,
(joint with Xiaojun Huang, Jin Lu and Xiaomin Tang), Advances in Mathematics , 374, 107388 (2020).
A high order Hopf lemma for mappings into classical domains and applications,
Comm. Anal. Geom. , 29 (2021), 1937-1977.
Algebraicity of the Bergman kernel, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv: 2007.00234.
On the classification of normal Stein spaces and finite ball quotients with Bergman-Einstein metrics,
(joint with Peter Ebenfelt and Hang Xu), Int. Math. Res. Not.(IMRN) , doi.org/10.1093/imrn/rnab120.
Holomorphic mappings between hyperquadrics with positive signature, (joint with Xiaojun Huang), Pure and Applied Math. Quarterly , 18 (2022), 599-616.
Proper mappings between indefinite hyperbolic spaces and type I classical domains,
(joint with Xiaojun Huang, Jin Lu and Xiaomin Tang), to appear in Trans. Amer. Math. Soc., https://doi.org/10.1090/tran/8618, [PDF].
A theorem on Hermitian rank and mapping problems, to appear in Math. Res. Lett. , [PDF].
Holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains, to appear in Crelle's Journal ,
Algebraic Bergman kernels and finite type domains in C^2, (joint with Peter Ebenfelt and Hang Xu), to appear in Indiana Univ. Math. J. , arXiv: 2111.07175.
Kähler-Einstein metrics and obstruction flatness of circle bundles, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv:2208.13367.
A new Poincar\'e type rigidity phenomenon with applications, submitted, [PDF].
Kähler-Einstein metrics and obstruction flatness II: unit sphere bundles, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv:2303.06408.
National Science Foundation CAREER grant DMS-2045104, 2021-2026.
National Science Foundation grant DMS-1800549, 2018-2021.
Named to list of teachers ranked as excellent by their students, UIUC, 2015, 2016, 2017.
Fall 2012, TA Teaching Excellence Award, Rutgers University.
Spring 2015, AMS Student Chapter Excellent Research Award at Rutgers University.
Co-organizer: A math summer program for high school students [Program link], summer, 2023.
Co-organizer: A math summer program for high school students [Program link], summer, 2022.
Co-organizer: A high school math teaching program [Program link], 2021-2022.
Co-organizer: Virtual Conference on Several Complex Variables, August 2020.
Co-organizer: Tianyuan International Conference in Several Complex Variables, Changchung, China,
Co-organizer: Special Session on Several Complex Variables at AMS Spring Central and Western
Joint Sectional Meeting, Honolulu, HI, March 2019.
Co-organizer: Southern California Analysis and PDE conference (SCAPDE), University of California, San Diego, San Diego, CA, 2018.
Co-organizer: AMS Fall Eastern Sectional Meeting, Special Session on CR geometry and PDE in complex analysis, SUNY Buffalo, Buffalo, NY, 2017.
Co-organizer: International Workshop in Several Complex Variables at Jilin Normal University, Changchun, China, 2017
Co-organizer: International Workshop in Complex Geometry at Capital Normal University, Beijing, China, 2016
Co-organizer: Several Complex Variables and CR Geometry seminar, UIUC
Led an Illinois Geometry Lab research project at UIUC, Fall 2015
June 2022, Several Complex Variables Seminar (online), IBS Center for Complex Geometry, Korea.
January 2022, AMS Special Session on Several Complex Variables, Geometric PDE and CR geometry, Joint Mathematics Meetings, Seattle, WA (changed to online).
October, 2021, Brazilian Webinar on Approximation Theory, Harmonic Analysis and related topics (online), Brazil.
March, 2021, PDE and Differential Geometry Seminar (online), University of Connecticut, CT.
March, 2021, Seminar semiklassische Analysis und Darstellungstheorie (online), University of Cologne, Germany.
November 2017, AMS Fall Western Sectional Meeting, Special Session on Several Complex Variables, University of California-Riverside, Riverside, CA.
October 2017, Midwest Workshop on Asymptotic Analysis, IUPUI, Indianapolis, IN.
August 2017, 9th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brazil.
January 2017, International Conference in Several Complex Variables and Partial Differential Equations, Texas A&M Univ. at Qatar, Doha, Qatar.
May 2016, Midwest Several Complex Variables Conference, University of Toledo,Toledo,OH.
April 2016, AMS Spring Western Sectional Meeting, Special Session on CR geometry and Partial Differential Equations in Complex Analysis,
University of Utah, Salt Lake City, UT.
January 2016, International Conference on PDE, Complex Analysis and Related Topics, Florida International University, Miami, FL.
May 2015, Analysis Seminar. University of California-San Diego, San Diego, CA.
April 2015, Analysis Seminar. University of California-Irvine, Irvine, CA.
January 2015, International Conference on Several Complex Variables, Texas A&M Univ. at Qatar, Doha, Qatar.
November 2014, Analysis Seminar, Temple Univ., Philadelphia, PA.
October 2014, AMS Fall Western Sectional Meeting, Special Session on Recent Progress in Harmonic Analysis and Complex Variables, San Francisco State University, San Francisco, CA.
September 2014, Analysis Seminar, Syracuse University, Syracuse, NY.
May 2014, International Conference on Complex Analysis and Geometry, Wuhan University, Wuhan, Hubei, China.
March 2014, AMS Spring Eastern Sectional Meeting, Special Session on Interaction between Complex and Geometric Analysis, Univ. of Maryland, Baltimore, MD.
October 2013, AMS Fall Eastern Sectional Meeting, Special Session on Several Complex Variables and CR geometry, Temple University, Philadelphia, PA.