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), to appear in Adv. Math., 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. [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), submitted [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), submitted.