About me:

I obtained my undergraduate degree (M.Math.) at Wadham College, Oxford University in 2007, and graduate degree (Ph.D.) at Cornell University in 2013. My Ph.D. supervisor is Dan Barbasch.

My area of research is on representation theory of reductive Lie groups. More precisely, I use the atlas computer program to study the unitary dual of real reductive groups, as well as their p-adic counterparts.

My publications can be found here. Notes of some of the courses I taught can be found here.

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 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
3. (with H. Zhang) The Unitary Dual of U(n,2), International Mathematics Research Notices IMRN 14 (2024), 10678 – 10707
4. On some conjectures of the unitary dual of U(p,q), Adavances in Mathematics 442 (2024), 109584
5. (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
6. (with C.P. Dong) Dirac Series of GL(n,R), International Mathematics Research Notices IMRN 12 (2023), 10702–10735
7. Unipotent representations of exceptional Richardson orbits, Journal of Lie Theory 33 (2023), No. 4, 1087-1111
8. (with C.P. Dong) Dirac Series for Complex E7, Forum Mathematicum 34(4) (2022), 1033–1049
9. (with C.P. Dong) Dirac index of some unitary representations of Sp(2n,R) and SO*(2n), Journal of Algebra 603 (2022), 1 - 37
10. (with C.P. Dong) Scattered Representations of Complex Classical Lie Groups, International Mathematics Research Notices IMRN 14 (2022), 10431–10457
11. (with D. Barbasch and C.P. Dong) Dirac series for complex classical Lie groups: A multiplicity-one theorem, Advances in Mathematics 403 (2022), 108370
12. (with C.P. Dong) On the Dirac Series of U(p,q), Mathematische Zeitschrift 298 (2021), 839 - 859
13. (with C.P. Dong) Scattered Representations of SL(n,C), Pacific Journal of Mathematics 309 (2020), No. 2, 289 - 312
14. (with J-S. Huang) A Casselman-Osborne Theorem for Rational Cherednik Algebras, Transformation Groups 23(1) (2018), 75 - 99
15. Some Calculations of the Lusztig-Vogan bijection for Classical Nilpotent Orbits, Journal of Algebra 487 (2017), 317 - 339
16. On Quantization of a Nilpotent Orbit Closure in G2, Proceedings of the American Mathematical Society 144 (2016), 5097 - 5102
17. Quantization of Special Symplectic Nilpotent Orbits and Normality of their Closures, Journal of Algebra 462 (2016), 37 - 53
18. Regular Functions of Symplectic Spherical Nilpotent Orbits and their Quantizations, Representation Theory 19 (2015), 333 -346

Preprints:

1. (with D. Barbasch) On the Dirac series of E8
2. (with C.P. Dong) Vogan's FPP conjecture for complex groups
3. (with H. Zhang) The genuine unitary dual of complex Spin groups

Teaching experiences:

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

‧ Abstract Algebra I (MAT 3004)
‧ Abstract Algebra II (MAT 3005)
‧ Real Analysis (MAT 3006)
‧ Advanced Linear Algebra (MAT 3040)
‧ Honours Linear Algebra II (MAT 3042)
‧ Geometry and Topology (MAT 4002)
‧ Differential Geometry (MAT 4033)
‧ Galois and Algebraic Number Theory (MAT 5210)

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

‧ Calculus I (MATH 1013)
‧ Calculus II (MATH 1014)
‧ Introduction to Matrix Algebra (MATH 2111)
‧ Lie Groups and Lie Algebras (MATH 5145)

Cornell University (2010, 2018)

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

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