Research

Published

30. L. Li, Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras, Journal of Algebra, Volume 634, 15 November 2023, Pages 97-164. (The arXiv version arXiv:2208.12307)

29. J. Glidewell, W. E. Hurst, K. Lee, L. Li, On the two-dimensional Jacobian conjecture: Magnus' formula revisited, III.  Contemporary Mathematics, Volume 791, 2024. (preprint)

28. K. Lee, L. Li, M. Rabideau, R. Schiffler, On the ordering of the Markov numbers,  Advances in Applied Mathematics, 143 (2023), Paper No. 102453. (The arXiv version) (Errata)

27. W. E. Hurst, K. Lee, L. Li, G. D. Nasr, On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I , to appear in Rocky Mountain Journal of Mathematics,  (The arXiv version) (Errata)

26. S. Han, K. Lee, L. Li, N. Loehr, Chain decompositions of $q,t$-Catalan numbers: tail extensions and flagpole partitions,  Annals of Combinatorics, 26 (2022), no. 3, 701–755.  (The arXiv version)

25. L. Li, J. Mixco, B. Ransingh, A. K. Srivastava,  An Introduction to Supersymmetric Cluster Algebras, Electronic Journal of Combinatorics 28(1) (2021), #P1.30. 

24. K. Lee, L. Li, R. Schiffler,  Newton polytopes of rank 3 cluster variables, Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1293-1330. (The arXiv version)

23. S. Han, K. Lee, L. Li, N. A. Loehr,  Chain decompositions of q,t-Catalan numbers via local chains, Ann. Comb. 24 (2020), no. 4, 739-765. (The arXiv version)

22. K. Lee, L. Li, M. Mills, R. Schiffler, A. Seceleanu, Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers, Advances in Mathematics, Volume 367, 24 June 2020, 107130. (The arXiv version)

21. K. Sweet, L.Li, E. Cheng, L. Liptak, D. E. Steffy, A complete classification of which $(n,k)$-star graphs are Cayley graphs, Graphs and Combinatorics. 34 (2018), no.1, 241--260. (The arXiv version)

20. M. de Cataldo, T. Haines, L. Li, Frobenius semisimplicity for convolution morphisms, Mathematische Zeitschrift, 289 (2018), no. 1-2, 119--169. (The arXiv version) (Errata, see in section 12 of [Haines])

19. K. Lee, L. Li, N. Loehr, A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers, SIAM J. Discrete Math (SIDMA). 32 (2018) no.1, 191--232 (The arXiv version) (The Sage code that helps with the computation.)

18. K. Lee, L. Li, B. Nguyen, New Combinatorial Formulas for Cluster Monomials of Type A Quivers, Electronic Journal of Combinatorics 24(2) (2017), #P2.42.

17. E. Cheng, L. Li, L. Liptak, S. Shim, D. E. Steffy, On the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs, Graphs and Combinatorics, 33 (2017), no. 1, 85-102. 

16. K. Lee, L. Li, D. Rupel, A. Zelevinsky, The existence of greedy bases in rank 2 quantum cluster algebras, Advances in Mathematics, 300 (2016), 360-389. (The arXiv version)

15. K. Lee, L. Li, M. Mills, A Combinatorial Formula for Certain Elements of Upper Cluster Algebras, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 11 (2015), 049, 24 pages. (The arXiv version)

14. K. Lee, L. Li, D. Rupel, A. Zelevinsky, Greedy bases in rank 2 quantum cluster algebras, Proceedings of the National Academy of Sciences of the United States of America (PNAS), 2014, vol.111, no.27, 9712--9716.

13. K. Lee, L. Li, A. Zelevinsky, Positivity and tameness in rank 2 cluster algebras, J. Algebraic Combin. 40 (2014), no. 3, 823--840. (The arXiv version)

12. K. Lee, L. Li, N. Loehr, Combinatorics of certain higher q,t-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula, Journal of Algebraic Combinatorics 39 (2014), no. 4, 749--781. (The arXiv version,)

11. K. Lee, L. Li, On natural maps from strata of quiver Grassmannians to ordinary Grassmannians, Contemporary Mathematics, volume 592, 2013, 199--214. (The arXiv version,)

10. K. Lee, L. Li, A. Zelevinsky, Greedy elements in rank 2 cluster algebras, Selecta Mathematica. New Series, 20 (2014), no. 1, 57--82. (The arXiv version)

9. K. Lee, L. Li, N. Loehr, Limits of Modified Higher (q,t)-Catalan Numbers , Electronic Journal of Combinatorics 20(3) (2013), #P4.

8. A. Yong, L. Li, Kazhdan-Lusztig polynomials and drift configurations, Algebra Number Theory 5 (2011), no. 5, 595--626. (The arXiv version)

7. A. Yong, L. Li, Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties , Advances in Mathematics 229 (2012), no. 1, 633--667. (The arXiv version,)

6. K. Lee, L. Li, $q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\mathbb{C}^2)^n$, Electronic Journal of Combinatorics 18 (2011), no. 1.

5. K. Lee, L. Li, On the diagonal ideal of $(\mathbb{C}^2)^n$ and $q,t$-Catalan numbers, DMTCS Proceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 881--888.

4. W. Hu, L. Li, Lawson homology, morphic cohomology and Chow motives, Mathematische Nachrichten, Volume 284, Issue 8-9, pages 1024--1047, June 2011. (The arXiv version)

3. L. Li, Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications, Michigan Mathematical Journal 58 (2009), no. 2, 565--598.

2. L. Li, Wonderful compactifications of arrangements of subvarieties , Michigan Mathematical Journal 58 (2009), no. 2, 535--563.

1. L. Li, W. Hu, The Lawson homology for Fulton-MacPherson configuration spaces, Algebraic & Geometric Topology 9 (2009) 455--471. 

Preprint

L. Li, S.K. Roushon, The affine Artin group of type $\widetilde{B}_n$ is virtually poly-free, arXiv:2403.09533
L. Li, Bipartite Determinantal Ideals and concurrent vertex maps, arXiv:2306.01947  (The  Sage code )
J. Illian, L. Li, Gröbner bases for the double determinantal ideals, arXiv:2305.01724

J. Glidewell, W. E. Hurst, K. Lee, L. Li, On the two-dimensional Jacobian conjecture: Magnus' formula revisited, II, arXiv:2205.12792

N. Hao, L. Li,  Higher cohomology of the pluricanonical bundle is not deformation invariant, 2006, arXiv:math/0612006

Ph.D. Thesis

L. Li, Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications (2006).