Research

Members

• Prof. X. He
  Algebraic groups, representation theory and arithmetic geometry
• Prof. Y.K. Lau
  Analytic number theory, automorphic forms, L-functions
• Dr. K.Y. Chan
  Langlands Program, Representation Theory, Algebaic groups, Hecke algebras
• Dr. C.Y. Hui
  Algebraic number theory, arithmetic geometry and algebra
• Dr. B. Kane
  Number theory, combinatorics
• Dr. X. Zhang
  Analytic Number Theory, Homogeneous Dynamical Systems, Linear Algebraic Groups
• Dr. A. Heleodoro, Postdoctoral Fellow
  Derived algebraic geometry and geometric representation theory
• Dr. R. La, Postdoctoral Fellow
  Representations of reductive p-adic groups, affine Hecke gebras, Generalised Springer correspondence
• Dr. W. Lee, Postdoctoral Fellow
  Automorphic forms, L-functions, Galois representations
• Dr. Z. Ran, Postdoctoral Fellow
  Diophantine geometry, theory of heights, Drinfeld modules, shtukas
• Dr. F. Schremmer, Postdoctoral Fellow
  Affine Weyl Groups, affine Deligne-Lusztig varieties, Iwahori-Hecke algebras, quantum Bruhat graphs and generalizations
• Dr. Q. Yu, Postdoctoral Fellow
  Algebraic group, representation theory, affine Deligne-Lusztig variety
• Dr. H. Zhang, Postdoctoral Fellow
  Representation theory, Unitary dual, Branching laws
• Dr. W. Zhang, Postdoctoral Fellow
  Representation theory, (affine) quantum groups, quantum symmetric pairs, Iwahori-Hecke algebras

Activities

Selected Publications

• X. He, Cordial elements and dimensions of affine Deligne-Lusztig varieties, Forum Math. Pi , 9 (2021), e9.
• X. He and R. Zhou, On the connected components of affine Deligne-Lusztig varieties, Duke Math. J. , 169 (2020), no. 14, 2697--2765.
• X. He, Cocenters of p-adic groups, I: Newton decomposition, Forum Math. Pi , 6 (2018), e2.
• X. He, Some results on affine Deligne-Lusztig varieties, Proceedings of the International Congress of Mathematicians, Rio de Janeiro 2018. Vol. II. Invited lectures, 1345--1365, World Sci. Publ., Hackensack, NJ, 2018.
• Lau Y.-K., Ng M.H., Wang Y., Average bound toward the generalized Ramanujan conjecture and its applications on Sato-Tate laws for GL(n), International Mathematics Research Notices, 2022 (2022), p.5720-5744.
• Jiang Y.-J., Lau Y.-K., Lü G.-S., Royer E., Wu J., On Fourier coefficients of modular forms of half integral weight at squarefree integers, Math. Z., 293 (2020), p.789-808.
• Lau Y.-K. and Wang Y., Absolute values of L-functions for GL(n,R) at the point 1, Adv. Math., 335 (2018), p.759-808
• Lau Y.-K., Liu J., Wu J., Local Behavior of Arithmetical Functions with Applications to Automorphic L-Functions, International Mathematics Research Notices, 2017 (2017), p.4815-4839
• Kei Yuen Chan, Restriction of the general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case), Journal für die reine und angewandte Mathematik (Crelles Journal)
• Kei Yuen Chan, Homological branching law for (GL_n+1(F),GL_n(F)): projectivity and indecomposability, Invent. math., 225 (2021), p.299-345
• Kei Yuen Chan, Gordan Savin, A vanishing Ext-branching theorem for (GL_n+1(F),GL_n(F)), Duke Math. J., 170 (2021), p.2237 - 2261
• Kei Yuen Chan, Gordan Savin, Bernstein–Zelevinsky Derivatives: a Hecke Algebra Approach, International Mathematics Research Notices, 2019 (2019), p.731–760
• C.-Y. Hui, M. Larsen, Maximality of Galois actions for abelian and hyperkahler varieties, Duke Math. J., 169 (2020), p.1163-1207
• A. Cadoret, C.-Y. Hui, A. Tamagawa, Geometric monodromy - semisimplicity and maximality, Annals of Math., 186 (2017), p.205-236
• C.-Y. Hui, l-independence for compatible systems of (mod l) representations, Compos. Math., 151 (2015), p.1215-1241
• King Cheong Fung and Ben Kane, On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring, Mathematics of Computation, 87 (2018), p.501-514
• Kathrin Bringmann, Ben Kane, Steffen Loebrich, Ken Ono and Larry Rolen, On Divisors of Modular Forms, Advances in Mathematics, 329 (2018), p.541-554
• Kathrin Bringmann, Ben Kane, Daniel Parry, and Robert Rhoades, On the Andrews-Zagier asymptotics for partitions without sequences, Advances in Mathematics, 309 (2017), p.436-451
• Kathrin Bringmann and Ben Kane, A problem of Petersson about weight 0 meromorphic modular forms, Research in the Mathematical Sciences, 3 (2016), p.1-31
• X. Zhang, On Representation of Integers from Thin Subgroups of SL(2, ℤ) with Parabolics, International Mathematics Research Notices, September (2020), p.5611-5629
• A. Heleodoro, A remark on Lurie’s representability Theorem https://arxiv.org/abs/2212.13572
• A. Heleodoro, Prestacks of Tate type https://arxiv.org/abs/2010.08095
• A. Heleodoro, Determinant map for the prestack of Tate objects https://doi.org/10.1007/s00029-020-00604-3
• A. Heleodoro, On the normally ordered tensor product and duality for Tate objects http://www.tac.mta.ca/tac/volumes/33/13/33-13abs.html
• R. La. Maximality properties of generalised springer representations of SO(n), 2022. preprint arXiv: 2208.10633.
• W. Lee. The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series, Ramanujan J. 56 (2021), no. 3, 865–889
• F. Schremmer, Bin Dong, Xuhua He, Pengfei Jin and Qingchao Yu, Machine learning assisted exploration for affine Deligne-Lusztig varieties. http://arxiv.org/abs/2308.11355
• F. Schremmer, Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits. http://arxiv.org/abs/2306.05933
• F. Schremmer, Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra. http://arxiv.org/abs/2306.06873
• F. Schremmer, Generic Newton points and cordial elements. http://arxiv.org/abs/2205.02039
• X. He and Q. Yu, Dimension formula for the affine deligne-lusztig variety X(µ, b). Mathematische Annalen 379, 1747-1765(2021)
• H. Zhang, A generalization of Duflo's conjecture, J. Lie Theory 32 (2022), no. 2, 519–552.
• Y. Ding, H. Zhang, Dirac series of GL(n,H). Preprint, arXiv:2208.09903.
• K.-Y. Wong, H. Zhang, The genuine unitary dual of complex spin groups. Preprint, arXiv:2303.10803.
• K.-Y. Wong, H. Zhang, The unitary dual of U(n,2). Preprint, arXiv:2401.15660.
• W. Zhang, Relative braid group symmetries on i-quantum groups of Kac-Moody type, Selecta Math. 29 (2023), no. 4, Paper No. 59.
• W. Zhang, A Drinfeld type presentation of affine i-quantum groups II: split BCFG type, Lett. Math. Phys. 112 (2022), no. 5, Paper No. 89.

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