I am interested in noncommutative geometry and higher structures, especially their applications in Lie theory, representation theory, symplectic geometry and complex/algebraic geometry. The recent theme of my work is quantization, including both geometric quantization and deformation quantization, with applications in representation theory of reductive Lie groups.
Mackey analogy as deformation of D-modules,
Submitted. [arXiv]
Equivariant deformation quantization and coadjoint orbit method, joint with Naichung Conan Leung.
Duke Mathematical Journal, 170(8): 1781-1850 (1 June 2021).
DOI: 10.1215/00127094-2020-0066. [arXiv]
A geometric realisation of tempered representations restricted to maximal compact subgroups, joint with Peter Hochs and Yanli Song.
Mathematische Annalen, 378, 97–152 (2020).
DOI: 10.1007/s00208-020-02006-4. [arXiv]
Todd class via homotopy perturbation theory
Advances in Mathematics, Vol. 352 (2019), 297-325.
https://doi.org/10.1016/j.aim.2019.06.003. [arXiv]
A geometric formula for multiplicities of K-types of tempered representations, joint with Peter Hochs and Yanli Song.
Transactions of the American Mathematical Society, 372 (2019), 8553-8586.
https://doi.org/10.1090/tran/7857. [arXiv]
Mackey analogy via D-modules in the example of SL(2,R), joint with Qijun Tan and Yijun Yao.
International Journal of Mathematics Vol. 28, No. 7 (2017), 1750055.
https://doi.org/10.1142/S0129167X17500550. [arXiv]
Dolbeault dga and L-infinity algebroid of the formal neighborhood
Advances in Mathematics, Vol. 305 (2017), 1131–1162.
https://doi.org/10.1016/j.aim.2016.10.006. [arXiv]
Dolbeault dga of a formal neighborhood
Transactions of the American Mathematical Society 368 (2016), 7809-7843.
DOI: 10.1090/tran6646. [arXiv]
The Dolbeault dga of the formal neighborhood of a diagonal
Journal of Noncommutative Geometry 9 (2015), no. 1, 161 - 184.
DOI: 10.4171/JNCG/190. [arXiv]