Li Li
Associate Professor

Office: 350 MSC (formerly SEB)
Phone: 248-370-3447
Fax: 248-370-4184
E-mail: li2345@oakland.edu

Mailing address:
Department of Mathematics and Statistics
Oakland University
Rochester, Michigan 48309

For the information of the classes I am teaching, please log in Moodle. Here is a list of some Courses I taught.


My Research Interest

  • Cluster algebra and related geometry and combinatorics.

  • Algebra, Geometry and Combinatorics of Schubert varieties.

  • Algebra, Geometry and Combinatorics of points in the plane or in higher dimensional spaces, which include: the ideal defining the diagonal locus in (C^2)^n and the related combinatorial object such as q,t-Catalan numbers; Hilbert scheme of points on a Deligne-Mumford stack.

  • Algebro-geometrical, topological and combinatorial properties of the objects related to arrangement of subvarieties, including hyperplane arrangement and subspace arrangement; wonderful compactifications of arrangements of subvarieties;the relation of arrangement with the study of singularities.

  • The theory of Lawson homology and morphic cohomology.

  • Groups and Cayley graphs.
  • Preprint

    K. Lee, L. Li, M. Mills, R. Schiffler, A. Seceleanu, Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers, submitted.

    L. Li, J. Mixco, B. Ransingh, A. K. Srivastava, An approach toward supersymmetric cluster algebras, submitted.

    Research papers

    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.

    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.)

    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 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.

    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.

    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.

    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.

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

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

    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.

    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.

    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.

    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. (Note that the arXiv version has a slightly different title.)

    Others

    N. Hao, L. Li, Higher cohomology of the pluricanonical bundle is not deformation invariant.

    L. Li, Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications , Ph.D. Thesis.

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