About me:

I obtained my undergraduate degree at Wadham College, Oxford University in 2007, and graduate degree at Cornell University in 2013 under the supervision of 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.

You can find my list of publications below.

We have openings for Ph.D. students and postdoctoral fellows. Feel free to contact me if you are interested.

List of publications:

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

Preprints:

1. (with D. Barbasch) The Dirac series of E8
2. (with H. Zhang) The genuine unitary dual of complex Spin groups
3. (with C.-P. Dong) Vogan's FPP conjecture for complex 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)
‧ Topology and Geometry (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)
‧ Introduction to Lie Groups (MATH 5145)

Cornell University (2010, 2018)

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

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