I am now a faculty member at Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
My research focus on gauge theory and differential geometry, in particular, the Kapustin-Witten equations, Higgs bundles, special Lagrangian submanifolds and manifolds with special holonomy.
Papers and preprints
1. Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations,Math Research Letters, Vol.25, no.4.
2. A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole, Journal of Topology, Volume.12, Issue.3, 2019.
3. (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions, Geometry&Topology, Volume 23, Number 5 2019.
4. (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions II, Duke Math Journal, 169 (2020), no. 12, 2281–2335.
5. The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations, submitted, arXiv:1808.03886.
6. (with Thomas Walpuski)Hecke modifications of Higgs bundles and the extended Bogomolny equation, J. Geom. Phys. 146 (2019), 103487, 17 pp.
7. (with Rafe Mazzeo)Classification of Nahm pole solutions of the Kapustin-Witten equations on S1\times\Sigma\times R^+, to appear in Transactions of the American Mathematical Society.
8. (with Rafe Mazzeo)Opers and the twisted Bogomolny equations, to appear in Annales scientifiques de l'École normale supérieure
9. The behavior of sequences of solutions to the Hitchin-Simpson equations, arXiv:2002.08109.
10. On the Moduli Space of the Octonionic Nahm’s Equations, arXiv:2006.11625.
11. (with Yue Wang)Inference on autoregulation in gene expression, arXiv:2201.03164.
12. The Branched Deformation of the Speical Lagrangian Submanifolds, arXiv:2202.12282.
13. Existence of nondegenerate Z2 harmonic 1-forms via Z3 symmetry, arXiv:2202.12283.
Education
1. B.S. Peking University, 2009-2013
2. Ph.D. California Institute of Technology, 2013-2018, Thesis Advisor: Yi Ni, Ciprian Manolescu
Employment
1. Research Assistant Professor, Simons Center for Geometry and Physics, Stony Brook University, September 2018-Feb 2022
2. Associate Research, Academy of Mathematics and Systems Science, Chinese Academy of Science, March 2022-Present