Seung Jin Lee's Hompage

I am an associate professor at Seoul National University. I am interested in combinatorial problems connected with other areas such as symmetric functions, algebraic geometry, and representation theory. Some of my topics of interest: (double) affine Schubert polynomials, Schubert calculus, any kind of symmetric function (and other functions generalized to other LIe type) such as Macdonald polynomials, k-Schur functions and chromatic quasisymmetric functions, to name a few. Lusztig's q-weight multiplicities and their generalization. 

Here is my CV.

Email: lsjin[at]snu.ac.kr

Publications

- (with Jaeseong Oh and Donghyun Kim) Shuffle formula in science fiction for Macdonald polynomials,  Compositio Mathematica. 2025;161(5):1075-1127. doi:10.1112/S0010437X25007122

-Crystal structure on King tableaux and semistandard oscillating tableaux, Transformation Groups, 2023, https://doi.org/10.1007/s00031-023-09804-5

-(with Jaeseong Oh and B.  Rhoades) Haglund's conjecture for multi-t Macdonald polynomials, Discrete Mathematics, Volume 346, Issue 6, 2023,

-(with T. Lam and M. Shimozono) Back stable K-theory Schubert calculus, International Mathematics Research Notices, 2022, https://doi.org/10.1093/imrn/rnac315.

-(with T.Lam and M. Shimozono) On the coproduct in affine Schubert calculus, arXiv:1906.08118. LMS Lecture note series 473, Facets of algebraic geometry (Fulton 80 volume). 2 (2022)115--146.

- (with T. Lam and M. Shimozono) Back stable Schubert calculus, Compositio Math. 157 (2021), 883-962.

- Linear relations on LLT polynomials and their k-Schur positivity for k=2, Journal of Algebraic Combinatorics, 53 (2021), 973-990

- Positivity of Cylindric skew Schur functions, Journal of Combinatorial Theory, Series A, 168 (2019), 26-49.

- Combinatorial description of the cohomology of the affine flag variety, Transactions of the American Mathematical Society, 371 (2019), 4029-4057

- Chern class of Schubert cells in the flag manifold and related algebras, Journal of Algebraic Combinatorics, 2017, https://doi.org/10.1007/s10801-017-0773-3

- Combinatorial description of the cohomology of the affine flag variety, Extended abstract, Proceedings of FPSAC 2016, http://www.lix.polytechnique.fr/~pilaud/FPSAC16/final_83.

- Pieri rule for the affine flag variety, Extended abstract, Proceedings of FPSAC 2015, http://fpsac2015.sciencesconf.org/70975.

- Pieri rule for the affine flag variety, Advances in Mathematics, 304 (2017), 266-284.

- (with A. Barvinok and I. Novik) Explicit constructions of centrally symmetric k-neighborly polytopes and large strictly antipodal sets, 

Discrete & Computational Geometry, 49 (2013), 429--443. 

- (with A. Barvinok and I. Novik) Centrally symmetric polytopes with many faces, 

Israel Journal of Mathematics, Israel Journal of Mathematics, 195 (2013), 457--472. 

- (with A. Barvinok and I. Novik) Neighborliness of the symmetric moment curve, Mathematika, 59 (2013), 223--249. 

Preprints

- (with Hyunjae Choi and Donghyun Kim) Lusztig $q$-weight multiplicities and Kirillov-Reshetikhin crystals, arXiv:2412.20757.

- Combinatorial description of Lusztig $q$-weight multiplicity, arXiv:2409.02341.

- (with Jaeseong Oh and Donghyun Kim) Toward Butler's conjecture arXiv:2212.09419.

-(with Jaeseong Oh and Brendon Rhoades) Two conjectures for Macdonald polynomials: The stretching symmetry and Haglund's conjecture, arXiv:2203.04590

-(with Sue Kyong Y. Soh) Explicit formulas for e-positivity of chromatic quasisymmetric functions, arXiv:2201.13080.

- Local neighborliness of the symmetric moment curve, arXiv:1102.5143.