Research

Research

1. Representation theory, quantum groups, cluster algebras, combinatorics, semigroups. 

2. Applications of Grassmannian cluster algebras to scattering amplitudes in physics.

3. Tropical geometry and its application to statistics and machine learning. 

Preprints

1. Transitive and Gallai colorings (with  Ron Adin, Arkady Berenstein, Jacob Greenstein,  Avichai Marmor, and Yuval Roichman), arXiv:2309.11203.

2. On the simplicity of the tensor product of two simple modules of quantum affine algebras (with Léa Bittmann), arXiv:2203.17268.

3. Rigid indecomposable modules in Grassmannian cluster categories (with Karin Baur, Dusko Bogdanic, and Ana Garcia Elsener), arXiv:2011.09227.

4. Tropical Geometry, Quantum Affine Algebras, and Scattering Amplitudes (with Nick Early),  arXiv:2303.05618.

Publications 

link to MathSciNet

1. Clustering Cluster Algebras with Clusters (with Man-Wai Cheung, Pierre-Philippe Dechant, Yang-Hui He, Elli Heyes, Edward Hirst), arXiv:2212.09771, to appear in Advances in Theoretical and Mathematical Physics. 

2. Dual canonical bases for unipotent groups and base affine spaces, arXiv:2010.07060, to appear in the special JAA issue on Cluster Algebras and Related Topics.

3. Quasi-homomorphisms of quantum cluster algebras (with Wen Chang and Min Huang), Journal of Algebra, volume 638, 2024, 506--534.

4. Real roots in the root system $T_{2,p,q}$ (with Karin Baur and Andrei Smolensky), Journal of Lie Theory 33 (2023), No. 4, 1113--1138.

5. The amplituhedron crossing and winding numbers (with Xavier Blot), Journal of Geometry and Physics, 2023.

6. Equivariant multiplicities via representations of quantum affine algebras (with Elie Casbi), Sel. Math. New Ser. 29, 9 (2023).

7. Finite basis problem for the variety generated by all monoids of order five (with Bin Bin Han, Wen Ting Zhang), Communications in Algebra, Communications in Algebra, 51 (2023), 424--439.

8. Construction of rank 2 indecomposable modules in Grassmannian cluster categories (with Karin Baur and Dusko Bogdanic), Adv. Stud. Pure Math., 2023: 1--45 (2023).

9. Quantum affine algebras and Grassmannians (with Bing Duan, Wen Chang, and Chris Fraser), Mathematische Zeitschrift, 296 (2020), 1539--1583.

10. Quiver mutations and Boolean reflection monoids (with Bing Duan and Yan-Feng Luo),  Journal of Algebra, 544 (2020), 417--453.

11. The 4-CB algebra and sovable lattice models (with Vladimir Belavin, Doron Gepner, and Ran Tessler), J. High Energ. Phys. (2019) 2019: 155.

12. On cacti and crystals (with Arkady Berenstein and Jacob Greenstein),  In: M. Gorelik, V. Hinich, A. Melnikov (eds) Representations and Nilpotent Orbits of Lie Algebraic Systems, Progress in Mathematics, vol 330 (2019), Birkh\"{a}user, Cham.

13. Cluster algebras and snake modules (with Bing Duan and Yan-Feng Luo), Journal of Algebra, 519 (2019), 325--377.

14. Three-term recurrence relations of minimal affinizations of type $G_2$ (with Li Qiao), Journal of Lie Theory 27 (2017), No. 4, 1119--1140.

15. Graded limits of minimal affinizations over the quantum loop algebra of type $G_2$ (with Katsuyuki Naoi), Algebras and Representation Theory, 19 (2016), 957--973.

16. M-systems and cluster algebras (with Qian-Qian Zhang, Bing Duan, and Yan-Feng Luo), Int. Math. Res. Not. IMRN 2016, no. 14, 4449--4486.

17. On the extended T-system of type $C_3$, J. Algebraic Combin. 41 (2015), no. 2, 577--617.

18. On the variety generated by all $n$-element semigroups (with Wen Ting Zhang and Yan Feng Luo), Algebra universalis, 73 (2015), 225--248.

19. Classification of finitely based words in a class of words over a $3$-letter alphabet (with Yan-Feng Luo), Semigroup Forum, 91 (2015), 200--212.

20. The variety generated by all $4$-element monoids is finitely based (with Edmond W. H. Lee), Glasnik Matematicki, 50 (2015), no. 2, 373--396.

21. Extended T-system of type $G_2$ (with Eugene Mukhin), SIGMA 9 (2013), 054, 28 pages. pdf.

22. XXZ Bethe ansatz equations and spaces of quasi-polynomials (with Vitaly Tarasov), 2013 J. Phys.: Conf. Ser. 411 012020 doi:10.1088/1742-6596/411/1/012020. pdf.

23. On the finite basis problem for certain $2$-limited words (with Wen Ting Zhang and Yan Feng Luo), Acta Mathematica Sinica, English Series, 29 (2013), 571--590. pdf.

24. Hereditarily Finitely Based Semigroups of Triangular Matrices over Finite Fields (with Wen Ting Zhang and Yan Feng Luo), Semigroup Forum, 86 (2013), 229--261.

25. Minimal non-finitely based semigroups (with Edmond W. H. Lee and Wen Ting Zhang), Semigroup Forum, 85 (2012), Issue 3, 577--580.

26. On the variety generated by the monoid of triangular $2\times 2$ matrices over the two-element field (with Wen Ting Zhang and Yan Feng Luo), Bull. Aust. Math. Soc. 86 (2012), 64--77.

27. On the finite basis problem for the monoids of triangular boolean matrices (with Yan Feng Luo), Algebra Universalis 65 (2011), 353--362. pdf.

28. Minimal non-finitely based monoids (with Edmond W. H. Lee), Dissertationes Mathematicae 475 (2011), 65 pp.

29. Equational property of certain transformation monoids (with Yan Feng Luo), Int. J. Algebra Comput. 20(6) (2010), 833--845.