Kyungyong Lee
Mathematician
Mathematician
Kyungyong Lee, Ph.D.
Email : kyungyong.lee@ua.edu; klee1@kias.re.kr
Selected papers
Scattering diagrams, tight gradings, and generalized positivity (with Amanda Burcroff and Lang Mou), PNAS, 122 (18) e2422893122.
Positivity for cluster algebras (with Ralf Schiffler), Annals of Math. (2015) 73--125.
Proof of a positivity conjecture of M. Kontsevich on noncommutative cluster variables (with Ralf Schiffler), Compositio Math. (2012), 1821--1832.
Local syzygies of multiplier ideals (with Robert Lazarsfeld), Inventiones Math. (2007), 409--418.
The other research papers and preprints (under construction)
Positivity of generalized cluster scattering diagrams (with Amanda Burcroff and Lang Mou), arXiv:2503.03719
Geometry of C-vectors and C-Matrices for mutation-infinite quivers (with Tucker Ervin, Blake Jackson and Son Dang Nguyen), arXiv:2410.08510
An unexpected property of g-vectors for rank 3 mutation-cyclic quivers (with Jihyun Lee), arXiv:2409.00599
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, IV (with Li Li), arXiv:2408.01279
An explicit description for quiver Grassmannians of the Kronecker quiver (with Ulysses Alvarez), arXiv:2403.19804
Broken lines and compatible pairs for rank 2 quantum cluster algebras (with Amanda Burcroff), arXiv:2404.14369
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, III (with Jacob Glidewell, William E. Hurst and Li Li), Contemporary Mathematics, Volume 791 (2024).
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, II (with Jacob Glidewell, William E. Hurst and Li Li), arXiv:2205.12792
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I (with William E. Hurst, Li Li and George D. Nasr), Rocky Mountain J. Math. (2023) 791--806.
On the ordering of the Markov numbers (with Li Li, Michelle Rabideau and Ralf Schiffler), Advances in Applied Mathematics, (2023) 102453.
Geometric description of C-vectors and real Losungen (with Kyu-Hwan Lee and Matthew R. Mills), Mathematische Zeitschrift (2023) Article number: 44.
Permutations whose reverse shares the same recording tableau in the RSK correspondence (with T. J. Ervin, B. Jackson, J. Lane, S. Nguyen, J. O'Donohue and M. Vaughan), Seminaire Lotharingien de Combinatoire (2022), Article B86a.
Chain decompositions of q,t-Catalan numbers III: tail extensions and flagpole partitions (with Seongjune Han, Li Li and Nicholas A. Loehr), Annals of Combinatorics (2022), 701--755.
A combinatorial formula for Kazhdan-Lusztig polynomials of sparse paving matroids (with George D. Nasr and Jamie Radcliffe), Electron. J. of Combin. (2021) DOI: https://doi.org/10.37236/10602.
A Combinatorial Formula for KazhdanLusztig Polynomials of ρ-Removed Uniform Matroids (with George D. Nasr and Jamie Radcliffe), Electron. J. of Combin. (2020) DOI: https://doi.org/10.37236/9435
Newton polytopes of rank 3 cluster variables (with Li Li and Ralf Schiffler), Algebraic Combinatorics (2020).
Chain Decompositions of q,t-Catalan Numbers via Local Chains (with Seongjune Han, Li Li and Nicholas A. Loehr), Annals of Combinatorics (2020), 739--765.
Cluster algebras and Jones polynomials (with Ralf Schiffler), Selecta Math. (2019) Article number: 58.
Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers (with Li Li, Matthew Mills, Ralf Schiffler and Alexandra Seceleanu), Adv. Math. (2020), 107--130.
Rigid reflections and Kac-Moody algebras (with Kyu-Hwan Lee), Sci. China Math. (2019), 1317--1330.
A correspondence between rigid modules over path algebras and simple curves on Riemann surfaces (with Kyu-Hwan Lee), Experimental Math. 10.1080/10586458.2018.1538910.
A Combinatorial Approach to the Symmetry of q,t-Catalan Numbers (with Li Li and Nicholas A. Loehr), SIAM J. Discrete Math. (2018) 191--232.
New combinatorial formulas for cluster monomials of type A quivers (with Li Li and Ba Nguyen), Electron. J. of Combin. (2017), #P2.42.
A combinatorial approach to root multiplicities of rank $2$ hyperbolic Kac-Moody algebras (with Seok-Jin Kang and Kyu-Hwan Lee), Comm. Algebra. (2017) 4785--4800.
The existence of quantum greedy bases in rank 2 cluster algebras (with Li Li, Dylan Rupel and Andrei Zelevinsky), Adv. Math. (2016), 360--389.
A combinatorial formula for certain elements of upper cluster algebras (with Li Li and Matthew R. Mills), SIGMA (2015), 049.