About me:

I am currently an Associate Professor at the Chinese University of Hong Kong, Shenzhen. I obtained my Master degree at Wadham College, Oxford University in 2007, and Ph.D. degree at Cornell University in 2013.

My area of research is on representation theory of reductive Lie groups. You can also find the notes of some of the courses I taught here.

Here are some small projects I carried out with the help of artificial intelligence:

List of publications:

  1. (with K.Y. Chan) On the Lefschetz principle for GL(n,C) and GL(m,Qp), Israel Journal of Mathematics, to appear
  2. (with C.P. Dong) Vogan's FPP conjecture for complex groups, Transactions of the American Mathematical Society 379(2) (2026), 867 - 884
  3. (with D. Barbasch) Admissible modules and normality of classical nilpotent varieties, Festschrift in honor of Toshiyuki Kobayashi, Progress in Mathematics 357, Volume 1 (2025), 165 - 197
  4. (with H. Zhang) The Unitary Dual of U(n,2), International Mathematics Research Notices IMRN 14 (2024), 10678 – 10707
  5. On some conjectures of the unitary dual of U(p,q), Advances in Mathematics 442 (2024), 109584
  6. (with J.-S. Huang and H. He) Transfer of unitary highest weight modules and small unipotent representations, Acta Mathematica Sinica (English Series) 40(3) (2024), 772-791
  7. (with C.P. Dong) Dirac Series of GL(n,R), International Mathematics Research Notices IMRN 12 (2023), 10702–10735
  8. Unipotent representations of exceptional Richardson orbits, Journal of Lie Theory 33 (2023), No. 4, 1087-1111
  9. (with C.P. Dong) Dirac Series for Complex E7, Forum Mathematicum 34(4) (2022), 1033–1049
  10. (with C.P. Dong) Dirac index of some unitary representations of Sp(2n,R) and SO*(2n), Journal of Algebra 603 (2022), 1 - 37
  11. (with C.P. Dong) Scattered Representations of Complex Classical Lie Groups, International Mathematics Research Notices IMRN 14 (2022), 10431–10457
  12. (with D. Barbasch and C.P. Dong) Dirac series for complex classical Lie groups: A multiplicity-one theorem, Advances in Mathematics 403 (2022), 108370
  13. (with C.P. Dong) On the Dirac Series of U(p,q), Mathematische Zeitschrift 298 (2021), 839 - 859
  14. (with C.P. Dong) Scattered Representations of SL(n,C), Pacific Journal of Mathematics 309 (2020), No. 2, 289 - 312
  15. (with J-S. Huang) A Casselman-Osborne Theorem for Rational Cherednik Algebras, Transformation Groups 23(1) (2018), 75 - 99
  16. Some Calculations of the Lusztig-Vogan bijection for Classical Nilpotent Orbits, Journal of Algebra 487 (2017), 317 - 339
  17. On Quantization of a Nilpotent Orbit Closure in G2, Proceedings of the American Mathematical Society 144 (2016), 5097 - 5102
  18. Quantization of Special Symplectic Nilpotent Orbits and Normality of their Closures, Journal of Algebra 462 (2016), 37 - 53
  19. Regular Functions of Symplectic Spherical Nilpotent Orbits and their Quantizations, Representation Theory 19 (2015), 333 - 346

Preprints:

  1. Dirac cohomology of standard modules for real reductive groups
  2. Sommers duality and the Springer–Steinberg map for canonical left cells in types B and C
  3. (with W.-Y. Tsai and H. Zhang) Unitary Shimura Correspondence for Complex Classical Groups
  4. (with D. Barbasch) On the Dirac series of E8
  5. (with H. Zhang) The genuine unitary dual of complex Spin groups

Teaching experiences:

The Chinese University of Hong Kong, Shenzhen (2018 - present)

Hong Kong University of Science and Technology (2013 - 2017)

Cornell University (2010, 2018)

  • Calculus I (MATH 1110)
  • Introduction to Analysis (MATH 3110)