# Chul-hee Lee

I am a CMC fellow at the Korea Institute for Advanced Study. Korean page

## contact

**Email**: chlee@kias.re.kr

## research interests

- connections between number theory and mathematical physics
- modular forms and q-hypergeometric series
- representations of Lie algebras and quantum groups
- functional relations in integrable systems (Q-systems, T-systems and Y-systems)
- experimental mathematics and computer algebra systems

## research articles

- Spectrum of the Laplacian on the Fricke-Macbeath surface, arXiv:2311.02632)
- An explicit formula for the extended Gross-Keating datum of a quadratic form (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi), arXiv:1709.02772)
- On polyhedral formula for Kirillov-Reshetikhin modules, arXiv:1901.00104
- An inductive formula of the Gross-Keating invariant of a quadratic form. (joint with S. Cho, T. Ikeda, H. Katsurada and T. Yamauchi) Tohoku Mathematical Journal. (to appear)
- 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
- Computation of Gross-Keating invariants, arXiv:1809.10323

## 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