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),
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 into Levi-degenerate hypersurfaces,
(joint with Ilya Kossovskiy and Bernhard Lamel), to appear in Comm. Anal. Geom.,
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 high order Hopf lemma for mappings into classical domains and applications, to appear in
Comm. Anal. Geom. ,
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.