Career 2022.11-Present Vice President and Professor, ShanghaiTech University 2017.07-2022.11 President, Academy of Mathematics System Science, Chinese Academy of Science 2014.04-2017.10 Vice President, University of Chinese Academy of Sciences 2012.09-Present Dean, School of Mathematical Sciences, University of Chinese Academy of Sciences 2012.04 -2017.07 Academic President, Academy of Mathematics System Science, Chinese Academy of Science 1990.01-Present Research Assistant Professor, Research Associate Professor and Research Professor (1994), Institute of Mathematics, CAS 1988.07-1989.12 Post-doc, Institute of Mathematics, Chinese Academy of Sciences 1981.07-1982.08 Teacher, Huang Xi Kou High School, Hunan Province Education 1978.10-1981.07 Huaihua Institute 1982.09-1985.07 East China Normal University, M.S. in Mathematics 1985.09-1988.07 East China Normal University, Ph.D. in Mathematics
Research The primary research interests of Prof. Xi lie in algebraic groups and quantum groups. His research work includes a proof of Lusztig's conjecture on the based ring of a two-sided cell of an affine Weyl group of type A, confirming the necessary and sufficient conditions for validity of Deligne-Langlands conjecture for affine Hecke algebras. He proved that the properties of finite dimensional representations of a quantum group over a field of characteristic p>0 with parameter being a non-root of unity are similar to finite dimensional representations of an algebraic group over a field of characteristic 0 ; He gave a clear and explicit realization of finite dimensional irreducible representation of a quantum group at a root of unity; He constructed monomial bases of quantum groups (joint with V. Chari), computed some canonical bases and established a commutation formula for root vectors. Joint with Lusztig he discovered canonical left cells in affine Weyl groups, and joint with Tanisaki he proved that a geometric filtration of an affine Hecke algebra of type A coincides with an algebraic filtration of the affine Hecke algebra. He initiated the study of infinite dimensional abstract representations of algebraic groups. Selected Publications 1.Lusztig, G., Xi, N. (1988). Canonical left cells in affine Weyl groups. Adv. in Math., 72(2), 284-288. 2.Xi, N.(1990). Finite dimensional modules of some quantum groups over Fp (v). J. Reine Angew. Math, 410, 109-115. 3.Xi, N. (1994). Representations of affine Hecke algebras. Lecture Notes in Mathematics 1587，Springer-Verlag. 4.Xi, N. (1994). Root vectors in quantum groups, Comm. Math. Helv. 69 (1994), 612-639. 5.Xi, N. (1996). Irreducible modules of quantized enveloping algebras at roots of 1. Publ. of the Research Inst. for Math. Sci., 32(2), 235-276. 6.Chari, V., & Xi, N. (1999). Monomial bases of quantized enveloping algebras. Contemp. Math., 248, 69-82. 7.Xi, N. (2002). The Based Ring of Two-Sided Cells of Affine Weyl Groups of Type A n-1, Mem. of Amer. Math. Soc., Vol. 157, No. 749. 8.Tanisaki, T., & Xi, N. (2006). Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. Nagoya Math. J., 182, 285-311. 9.Xi, N. (2007). Representations of affine Hecke algebras and based rings of affine Weyl groups. J. of Ame. Math. Soc., 20(1), 211-217. 10.Xi, N. (2014).Some infinite dimensional representations of reductive groups with Frobenius maps, Sci. China Math. 57 (2014), No. 6, 1109-1120. 11. Basic Algebra, Volume 1 and Volume 2. Published in 2016 and 2018 respectively, and intended for freshman of math major at the University of Chinese Academy of Sciences; Basic Algebra, Volume 3. Published in 2021 and intended for sophomore of math major at the University of Chinese Academy of Sciences.
Major Awards and Honors 2001 Morningside Silver Medal 2005 The Chern Prize 2007 Second Prize of the National Natural Science Award 2009 Academician of Chinese Academy of Sciences 2021 Advanced individual of National teaching material construction
Public Services 2018.03-2023.03 Member of the 13th Standing Committee of the National Committee of the Chinese People's Political Consultative Conference 2020.01-2023.12 Vice Chairman of the 13th Council of the Chinese Mathematical Society |
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