### Research Interests

Generally speaking, I am interested in Representation Theory and Quantum Algebras.

More specifically, my current research interests are: Bethe ansatz method, Representation Theory of Quantum Groups, Lie Algebras and Superalgebras, and Integrable System.

### Preprints

**Solutions of \(\mathfrak{gl}_{m|n}\) XXX Bethe ansatz equation and rational difference operators**

(with Chenliang Huang, E. Mukhin), 28 Nov. 2018, (arXiv:1811.11225)**Fine gradings of complex simple Lie algebras and Finite Root Systems**

(with Gang Han, Jun Yu), 29 Oct. 2014. (arXiv:1410.7945)

### Publications

**On the Gaudin model of type \(G_2\)**

(with E. Mukhin), Commun. Contemp. Math. (arXiv:1711.02511)**Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root systems**

(with Gang Han, Yucheng Liu), Algebra Colloq.**26**:1 (2019) 123-138, (arXiv:1611.03943), to appear**Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus**

SIGMA**14**(2018), 046, 15 pages, (arXiv:1710.06534)**Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\)**

(with E. Mukhin, A. Varchenko), Pure Appl. Math. Q.**13**no.2 (2017), a special issue of in honor of Yuri Manin’s 80-th birthday, (arXiv:1705.02048)**On the Gaudin model associated to Lie algebras of classical types**

(with E. Mukhin, A. Varchenko), J. Math. Phys. 57, 101703 (2016) (arXiv:1512.08524)

My Erdös Number: 4.

Paul Erdős–>Shizuo Kakutani–>Karl Endel Petersen–>A. N. Varchenko–>Kang Lu