Admission Information

Recruit master's and doctoral students in algebra, welcome interested students!

Research interests

Geometric representation theory, Hall algebras, Quantum group, Canonical basis, Categorification, Schur-Weyl duality, Character sheaves.

Teaching

Topics in algebra-representation of quivers (Three times),
Abstract algebra I ( Five times),
Linear algebra (Twice),  
Probability and Statistics (Twice).

2016-2023 Spring

Abstract algebra II, 
Introduction to Lie algebra and its representations(Twice),
Representation of algebra,
Topology, 
Matrix analysis (Eight times).

Mentoring

Ph.D students
Jingjun Xing (2017) 
Shaolong Han (2019)
Bolong Tong (2019)
Jicheng Geng (2020)
Quanyong Chen (2020)
Ziqi Xing (2020)
Zhicheng Zhang (2021)
Jiaqi Huang (2022)
Wan Wu (2022)

Master students

Graduated students
Kevin (2019)
Jicheng Geng (2020)
David (2020)
Yubing Zhang (2021)
Nan Ten (2021)

Grants

(1)  Natural Science Foundation of Heilongjiang for Distinguished Young Scholars, China, Grant No. JQ2020A001, 2020-2023
(2)  National Nature Science Foundation of China, Grant No. 11671108, 2017-2020
(3)  Nature Science Foundation of Heilongjiang province, Grant No. LC2017001, 2017-2019
(4)  Fundamental Research Funds  for the central universities Grant No. GK2110260131, 2015-2018.
(5)  National Nature Science Foundation of China, Grant No. 12271120, 2023-2026

Selected Publications

(1) (Joint with C. Lai, Y. Li, L. Luo and W. Wang) Affine Hecke algebras and quantum symmetric pairs,  Mem. Amer. Math. Soc. 281 (2023), no. 1386, 99pp
(2) (Joint with C. Lai, Y. Li, L. Luo and W. Wang) Affine flag varieties and quantum symmetric pairs,  Mem. Amer. Math. Soc.  265 (2020), no. 1285, 123pp.

(3) (Joint with Y. Li) A geometric setting of quantum osp(1|2), Trans. Amer. Math. Soc. 367(2015), no. 11, 7895-7916.

(4) (Joint with Y. Li) Two-parameter quantum algebras, canonical bases and categorifications, Int. Math. Res. Notices, 16 (2015), 7016-7062.

(5) (Joint with Y. Li) Geometric Schur-Weyl duality of classical type II, Trans. Amer. Math. Soc, Series B. 2 (2015), 51-92.
(6) (Joint with S. Clark, Y. Li and W. Wang) Quantum supergroups III. Twistors, Comm. Math. Phys., 332 (2014), 415-436.

(7) (Joint with Y. Li) Positivity of canonical bases under comultiplication, Int. Math. Res. Notices, no. 9,6871-6931.

(8) (Joint with Y. Li) Affine flag varieties and quantum symmetric pairs, II. Multiplication formula, J. Pure Appl. Algebra  223 (2019), no. 10, 4311-4347.
(9) (Joint with Lai, Li, Luo, Wang and Watanabe) Quantum Schur duality of affine type C with three parameters, Math. Res. Let. 27 (2020), no. 1, 79-114.
(10) (Joint with J. Xing) Drinfeld double of deformed quantum algebra, Journal of algebra, 534(2019), 358-383
(11) (Joint with H. Ma and H. Xiao) Equivariant K-theory approach to i-quantum groups, Publ. Res. Inst.

Math. Sci. 58, no. 3, 635-668.

(12) (Joint with S. Kang, Y. Kim and B. Tong) Classical limit of Quantum Borcherds-Bozec Algebras, J. Pure Appl. Algebra, 2020:106502.
(13) (Joint with S. Kang, Y. Kim and B. Tong)  Abstract crystals for quantum Borcherds-Bozec algebras, J.

Lond. Math. Soc. (2) 104, no. 2, 803-822.
(14)  (Joint with S. Kang, Y. Kim and B. Tong)  Global bases for quantum Borcherds-Bozec algebras，Mathematische Zeitschrift, 2022，1-27.
(15) (Joint with B. Tong) Braid group actions of quantum Borcherds-Bozec algebras, Journal of algebra, 621 (2023), 92-115.
(16) (Joint with J. Geng and S. Han) Differential operator approach to i-quantum groups.  Acta Mathematica Sinica, English Series (to appear).
(17)  (Joint with  S. Han, S. Kang and Y. Kim) Perfect Basis Theory for Quantum Borcherds-Bozec Algebras
(18)  (Joint with  S. Han, S. Kang and Y. Shin) Young wall construction of level-1 highest weight crystals over U_q(D_4^{(3)}) and Uq(G^{(1)}_2), Journal of algebra (to appear).
(19)  (Joint with J. Geng and S. Han) Differential operator realization of braid group action on i-quantum groups
(20)  (Joint with  S. Han, S. Kang and Y. Kim) A New Young Wall Realization of  B(\lambda) and B(\infty), Algebra Colloquium 30 (2023), No. 3  503–540.

Selected talks

(1) Geometric approach to quantum algebras, 15th National algebra conference in China, July, 2019
(2) Positivity of canonical bases under comultiplication, Shanghai Conference on Representation Theory, Dec. 2015

(3) Equivalence of representation categories of various quantum and super quantum groups, Summer School and Workshop on Lie Theory and Representation Theory IV, East China Normal University, July 2015
(4) Geometric approach to Schur-Weyl duality of type D, AMS Sectional Meeting, March 2015
(5) Geometric approach to Schur-Weyl duality of classical types, Tsinghua University, July 2014
(6) A geometric setting for quantum osp(1|2), AMS Sectional Meeting, Oct. 2013
(7)  Geometric approach to quantum algebras,  The 9th Congress of Chinese Mathematicians, Nangjing, July 2022
(8) BLM approach to quantum algebras and its generalization, The 7th National Congress of Rings and Algebra，Qinzhou, June 2023

Conference Organized
International conference on representation theory VIII, Harbin, July 8-12, 2019