Difference between revisions of "Chul-hee Lee"
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| − | I am | + | I am an AI Fellow (AI Assistant Professor) at the Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study. |
[[이철희|Korean page]] | [[이철희|Korean page]] | ||
| Line 9: | Line 9: | ||
==research interests== | ==research interests== | ||
| − | * | + | * automorphic forms |
| − | |||
* representations of Lie algebras and quantum groups | * representations of Lie algebras and quantum groups | ||
* functional relations in integrable systems (Q-systems, T-systems and Y-systems) | * functional relations in integrable systems (Q-systems, T-systems and Y-systems) | ||
| − | * experimental mathematics | + | * computational and experimental mathematics with AI-driven discovery |
==research articles== | ==research articles== | ||
| − | * Verlinde rings and cluster algebras arising from quantum affine algebras ( | + | ===preprints=== |
| − | * Harder's conjecture and Miyawaki lift (joint with H. Katsurada), ''Forum Mathematicum''( | + | * Karel's conjecture on Fourier coefficients of $E_7$ Eisenstein series, ''preprint''. |
| − | + | * Lean-GAP: A Dataset of Formalized Graduate Algebra Problems (with S. Lee, B.-H. Hwang, H. Lim, J. Hyun, I. Choi, Y. Park, J. Baek, H. Hong, K. Lee, J. Heo, H. Baik and K.-H. Lee), [https://arxiv.org/abs/2606.02588 arXiv:2606.02588] | |
| + | * An explicit formula for some vector-valued differential operator on Siegel modular forms and its applications (with T. Ikeda and H. Katsurada), preprint. [[Media:Differential_operator_degree_3.pdf|PDF]] | ||
| + | * Verlinde rings and cluster algebras arising from quantum affine algebras (joint with J.-R. Li and E. Park), preprint. [https://arxiv.org/abs/2412.14601 arXiv:2412.14601] | ||
| + | * Spectrum of the Laplacian on the Fricke-Macbeath surface, preprint. [https://arxiv.org/abs/2311.02632 arXiv:2311.02632] | ||
| + | |||
| + | ===publications=== | ||
| + | * On Polyhedral Formulas for Kirillov-Reshetikhin Modules, ''SIGMA'' 22 (2026), 064, [https://doi.org/10.3842/SIGMA.2026.064 doi:10.3842/SIGMA.2026.064] | ||
| + | * Harder's conjecture and Miyawaki lift (joint with H. Katsurada), ''Forum Mathematicum'' 38 (2026), no. 4, 1111–1137. [https://doi.org/10.1515/forum-2025-0204 doi:10.1515/forum-2025-0204] | ||
* An explicit formula for the extended Gross-Keating datum of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), ''Mathematics of Computation'' (2025), 94, 1503–1541, [https://doi.org/10.1090/mcom/4050 doi:10.1090/mcom/4050]. [https://arxiv.org/abs/1709.02772 arXiv:1709.02772] | * An explicit formula for the extended Gross-Keating datum of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), ''Mathematics of Computation'' (2025), 94, 1503–1541, [https://doi.org/10.1090/mcom/4050 doi:10.1090/mcom/4050]. [https://arxiv.org/abs/1709.02772 arXiv:1709.02772] | ||
| − | |||
* An inductive formula for the Gross–Keating invariant of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), ''Tohoku Mathematical Journal (2)'' (2025), 77 (1) 55 - 75. [https://doi.org/10.2748/tmj.20230426 doi:10.2748/tmj.20230426] | * An inductive formula for the Gross–Keating invariant of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), ''Tohoku Mathematical Journal (2)'' (2025), 77 (1) 55 - 75. [https://doi.org/10.2748/tmj.20230426 doi:10.2748/tmj.20230426] | ||
* Product formula for the limits of normalized characters of Kirillov-Reshetikhin modules, ''International Mathematics Research Notices'' (2021), 13 [https://doi.org/10.1093/imrn/rnz113 doi:10.1093/imrn/rnz113] [https://arxiv.org/abs/1807.11194 arXiv:1807.11194] | * Product formula for the limits of normalized characters of Kirillov-Reshetikhin modules, ''International Mathematics Research Notices'' (2021), 13 [https://doi.org/10.1093/imrn/rnz113 doi:10.1093/imrn/rnz113] [https://arxiv.org/abs/1807.11194 arXiv:1807.11194] | ||
| − | * An elliptic hypergeometric function approach to branching rules (joint with Eric M. Rains and S. Ole Warnaar), ''SIGMA'' (2020), 16 :142 [https://arxiv.org/abs/2007.03174 arXiv:2007.03174] | + | * An elliptic hypergeometric function approach to branching rules (joint with Eric M. Rains and S. Ole Warnaar), ''SIGMA'' (2020), 16 :142 [https://arxiv.org/abs/2007.03174 arXiv:2007.03174] |
* Linear recurrence relations in $Q$-systems via lattice points in polyhedra, ''Transformation Groups'' (2019) 24: 429, [https://link.springer.com/article/10.1007/s00031-018-9502-9 doi:10.1007/s00031-018-9502-9], [https://arxiv.org/abs/1602.02347 arXiv:1602.02347] | * Linear recurrence relations in $Q$-systems via lattice points in polyhedra, ''Transformation Groups'' (2019) 24: 429, [https://link.springer.com/article/10.1007/s00031-018-9502-9 doi:10.1007/s00031-018-9502-9], [https://arxiv.org/abs/1602.02347 arXiv:1602.02347] | ||
* Positivity and periodicity of $Q$-systems in the WZW fusion ring, ''Advances in Mathematics'', Volume 311, 30 April 2017, Pages 532-568, [http://doi.org/10.1016/j.aim.2017.02.031 doi:10.1016/j.aim.2017.02.031], [https://arxiv.org/abs/1302.1467 arXiv:1302.1467] | * Positivity and periodicity of $Q$-systems in the WZW fusion ring, ''Advances in Mathematics'', Volume 311, 30 April 2017, Pages 532-568, [http://doi.org/10.1016/j.aim.2017.02.031 doi:10.1016/j.aim.2017.02.031], [https://arxiv.org/abs/1302.1467 arXiv:1302.1467] | ||
| Line 37: | Line 42: | ||
===notes=== | ===notes=== | ||
* Minor corrections to Nipp's tables of quaternary quadratic forms, [https://arxiv.org/abs/1902.08459 arXiv:1902.08459] | * Minor corrections to Nipp's tables of quaternary quadratic forms, [https://arxiv.org/abs/1902.08459 arXiv:1902.08459] | ||
| − | |||
==education== | ==education== | ||
| Line 51: | Line 55: | ||
==etc== | ==etc== | ||
* [https://github.com/chlee-0 personal repository on GitHub] | * [https://github.com/chlee-0 personal repository on GitHub] | ||
| − | * developing a wiki-based [ | + | * developing a wiki-based [https://wiki.mathnt.net/index.php mathematics website] (in Korean) for fun |
Latest revision as of 14:07, 5 August 2026
I am an AI Fellow (AI Assistant Professor) at the Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study. Korean page
contact
- Email: chlee@kias.re.kr
research interests
- automorphic forms
- representations of Lie algebras and quantum groups
- functional relations in integrable systems (Q-systems, T-systems and Y-systems)
- computational and experimental mathematics with AI-driven discovery
research articles
preprints
- Karel's conjecture on Fourier coefficients of $E_7$ Eisenstein series, preprint.
- Lean-GAP: A Dataset of Formalized Graduate Algebra Problems (with S. Lee, B.-H. Hwang, H. Lim, J. Hyun, I. Choi, Y. Park, J. Baek, H. Hong, K. Lee, J. Heo, H. Baik and K.-H. Lee), arXiv:2606.02588
- An explicit formula for some vector-valued differential operator on Siegel modular forms and its applications (with T. Ikeda and H. Katsurada), preprint. PDF
- Verlinde rings and cluster algebras arising from quantum affine algebras (joint with J.-R. Li and E. Park), preprint. arXiv:2412.14601
- Spectrum of the Laplacian on the Fricke-Macbeath surface, preprint. arXiv:2311.02632
publications
- On Polyhedral Formulas for Kirillov-Reshetikhin Modules, SIGMA 22 (2026), 064, doi:10.3842/SIGMA.2026.064
- Harder's conjecture and Miyawaki lift (joint with H. Katsurada), Forum Mathematicum 38 (2026), no. 4, 1111–1137. doi:10.1515/forum-2025-0204
- An explicit formula for the extended Gross-Keating datum of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), Mathematics of Computation (2025), 94, 1503–1541, doi:10.1090/mcom/4050. arXiv:1709.02772
- An inductive formula for the Gross–Keating invariant of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), Tohoku Mathematical Journal (2) (2025), 77 (1) 55 - 75. doi:10.2748/tmj.20230426
- Product formula for the limits of normalized characters of Kirillov-Reshetikhin modules, International Mathematics Research Notices (2021), 13 doi:10.1093/imrn/rnz113 arXiv:1807.11194
- An elliptic hypergeometric function approach to branching rules (joint with Eric M. Rains and S. Ole Warnaar), SIGMA (2020), 16 :142 arXiv:2007.03174
- Linear recurrence relations in $Q$-systems via lattice points in polyhedra, Transformation Groups (2019) 24: 429, doi:10.1007/s00031-018-9502-9, arXiv:1602.02347
- Positivity and periodicity of $Q$-systems in the WZW fusion ring, Advances in Mathematics, Volume 311, 30 April 2017, Pages 532-568, doi:10.1016/j.aim.2017.02.031, arXiv:1302.1467
- Linear recurrence relations in $Q$-systems and difference $L$-operators, J. Phys. A: Math. Theor. 48 (2015), no. 19, 195201 doi:10.1088/1751-8113/48/19/195201 arXiv:1412.1638
- Nahm's conjecture and Y-systems, Commun. Number Theory Phys. 7 (2013), no.1, 1-14., doi:10.4310/CNTP.2013.v7.n1.a1, arXiv:1109.3667
- A proof of the KNS conjecture : $D_r$ case, J. Phys. A: Math. Theor. 46 (2013), no. 16, 165201, doi:10.1088/1751-8113/46/16/165201, arXiv:1210.1669
- A Note on Nahm's Conjecture in Rank 2 Case (joint with An Huang), Commun. Number Theory Phys. 4 (2010), no. 4, 609–622., doi:10.4310/CNTP.2010.v4.n4.a1arXiv:1008.4981
notes
- Minor corrections to Nipp's tables of quaternary quadratic forms, arXiv:1902.08459
education
- B.S. Mathematics, Seoul National University, Aug, 2006.
- Ph.D. Mathematics, University of California, Berkeley, May, 2012. (advisor: Richard E. Borcherds)
files
etc
- personal repository on GitHub
- developing a wiki-based mathematics website (in Korean) for fun