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 2017-Present 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), submitted. [PDF].
Complexity of holomorphic maps from the complex unit ball to classical domains, (joint with Yuan Yuan), to appear in Asian J. Math. (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), submitted.
Here is an expanded note for the submitted version[PDF].
A remark on Bergman-Einstein metrics, (joint with Xiaojun Huang), preprint. [PDF].
Regularity of CR mappings into Levi-degenerate hypersurfaces, (joint with Ilya Kossovskiy and Bernhard Lamel), to appear in Comm. Anal. Geom., [PDF].
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 wit John D'Angelo), to appear in Math. Res. Lett , arxiv: 1711.06539.
Regularity of mappings into classical domains, submitted, [PDF].
A high order Hopf lemma for mappings into classical domains and applications, submitted, [PDF].