publications

 
 
 

  publications -- all areas


  1. Joanna Bieri, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi and Tamara Veenstra, Murmurations, Mestre-Nagao sums, and Convolutional Neural Networks for elliptic curves, arXiv:2603.17681.

  2. Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver and Alexey Pozdnyakov, Murmurations: a case study in AI-assisted mathematics, arXiv:2603.09680.

  3. Xiaoyu Huang, Blake Jackson and Kyu-Hwan Lee, From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm, to apear in Sém. Lothar. Combin.

  4. Kyu-Hwan Lee and Seewoo Lee, Machines learn number fields, but how? The case of Galois groups, to appear in Res. Math. Sci.

  5. Kyu-Hwan Lee and Se-jin Oh, Quantum cluster algebra, braid moves and quantum virtual Grothendieck ring, to appear in Selecta Math. (N.S.).

  6. Il-Seung Jang, Kyu-Hwan Lee and Se-jin Oh, Braid group action on quantum virtual Grothendieck ring through constructing presentations, arXiv:2305.19471.

  7. Giorgi Butbaia, Kyu-Hwan Lee, and Fabian Ruehle, Interpretable machine learning for Kronecker coefficients, to appear in Adv. Theor. Math. Phys.

  8. Joanna Bieri, Giorgi Butbaia, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra, Machine learning the vanishing order of rational L-functions, to appear in Adv. Theor. Math. Phys.

  9. Angelica Babei, François Charton, Edgar Costa, Xiaoyu Huang, Kyu-Hwan Lee, David Lowry-Duda, Ashvni Narayanan, and Alexey Pozdnyakov, Learning Euler factors of elliptic curves, to appear in Adv. Theor. Math. Phys.

  10. Michael R. Douglas and Kyu-Hwan Lee, Mathematical data science, to appear in Adv. Theor. Math. Phys.

  11. Joanna Bieri, Giorgi Butbaia, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra, Learning Fricke signs from Maass form coefficients, to appear in Adv. Theor. Math. Phys.

  12. Kymani T. K. Armstrong-Williams, Edward Hirst, Blake Jackson and Kyu-Hwan Lee, Machine learning mutation-acyclicity of quivers, J. Comput. Algebra. 15 (2025) 100040.

  13. Kyu-Hwan Lee, Data-scientific study of Kronecker coefficients, Exp. Math. (2025).

  14. Kyu-Hwan Lee, Dongwen Liu and Thomas Oliver, Convergence of Kac-Moody Eisenstein series over a function field, Selecta Math. (N.S.) 31 (2025), no. 39.

  15. Kyu-Hwan Lee, Thomas Oliver and Alexey Pozdnyakov, Murmurations of Dirichlet characters, Int. Math. Res. Not. IMRN. 2025 (2025), no. 1, 1-28.

  16. Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver and Alexey Pozdnyakov, Murmurations of elliptic curves, Exp. Math. 34 (2025), no.3, 528-540.

  17. Lisa Carbone, Howard Garland, Kyu-Hwan Lee, Dongwen Liu and Stephen D. Miller, On the convergence of Kac-Moody Eisenstein series, Amer. J. Math. 146 (2024) no. 5, 1253-1274.

  18. Kyu-Hwan Lee, Machine-learning Kronecker coefficients, International Journal of Data Science in the Mathematical Sciences, 2 (2024), no.1, 79-86.

  19. Il-Seung Jang, Kyu-Hwan Lee and Se-jin Oh, Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras, Commun. Math. Phys. 405, 173 (2024).

  20. Jonathan D. Axtell and Kyu-Hwan Lee, Quantum generalized Kac-Moody algebras via Hall algebras of complexes, Proc. Sympos. Pure Math. 108 (2024).

  21. Gunhee Cho and Kyu-Hwan Lee, Equivalence of invariant metrics via Bergman kernel on complete noncompact Kähler manifolds, Math. Ann. 389 (2024), 3809-3839.

  22. Kyu-Hwan Lee and Se-jin Oh, Auto-correlation functions for unitary groups, Algebr. Represent. Theory 27 (2024), 583-611.

  23. Malik Amir, Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver and Eldar Sultanow, Machine learning class numbers of real quadratic fields, International Journal of Data Science in the Mathematical Sciences, 1 (2023), no. 2, 107-134.

  24. Jang Soo Kim, Kyu-Hwan Lee and Se-jin Oh, Weight multiplicities and Young tableaux through affine crystals, Mem. Amer. Math. Soc. 283, 1401 (2023).

  25. Kyu-Hwan Lee, Kyungyong Lee and Matthew R. Mills, Geometric description of c-vectors and real Lösungen, Math. Z. 303, 44 (2023).

  26. Yang-Hui He, Kyu-Hwan Lee and Thomas Oliver, Machine-learning invariants of arithmetic curves, J. Symb. Comput. 115 (2023), 478-491.

  27. Kyu-Hwan Lee and Jeongwoo Yu, Rigid reflections of rank 3 Coxeter groups and reduced roots of rank 2 Kac-Moody algebras, Algebr. Represent. Theory 26 (2023), 1465-1496.

  28. Yang-Hui He, Kyu-Hwan Lee and Thomas Oliver, Machine-learning number fields, Mathematics, Computation and Geometry of Data 2 (2022), 49-66.

  29. Lisa Carbone, Kyu-Hwan Lee and Dongwen Liu, Entirety of cuspidal Eisenstein series on Kac-Moody groups, Algebra Number Theory 16 (2022), no. 5, 1099-1119.

  30. Kyu-Hwan Lee and Se-jin Oh, Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters, Adv. Math. 401 (2022) 108309.

  31. Yang-Hui He, Kyu-Hwan Lee and Thomas Oliver, Machine-learning the Sato-Tate conjecture, J. Symb. Comput. 111 (2022), 61-72.

  32. Kyu-Hwan Lee, Dongwen Liu and Thomas Oliver, Character expansion of Kac-Moody correction factors, Pacific J. Math. 313 (2021), no.1, 159-183.

  33. Kyu-Hwan Lee and Kyungyong Lee, A correspondence between rigid modules over path algebras and simple curves on Riemann surfaces, Exp. Math. 30 (2021), no.3, 315-331.

  34. Gabriel Feinberg, Sungsoon Kim, Kyu-Hwan Lee and Se-jin Oh, Fully commutative elements of the complex reflection groups, J. Algebra 558 (2020), 371-394.

  35. Kyu-Hwan Lee and Jerzy Weyman, Some branching formulas for Kac-Moody Lie algebras, Commun. Korean Math. Soc. 34 (2019), no. 4, 1079-1098.

  36. Suh Hyun Choi, Chang Heon Kim, Yeong-Wook Kwon and Kyu-Hwan Lee, Rationality and p-adic properties of reduced forms of half-integral weight, J. Number Theory 204 (2019), 446-470.

  37. Kyu-Hwan Lee and Kyungyong Lee, Rigid reflections and Kac-Moody algebras, Sci. China Math. 62 (2019), no.7, 1317-1330.

  38. Kyu-Hwan Lee, Cristian Lenart and Dongwen Liu with appendix by Dinakar Muthiah and Anna Puskás, Whittaker functions and Demazure characters, J. Inst. Math. Jussieu 18 (2019), no.4, 759-781.

  39. Kyu-Hwan Lee and Se-jin Oh, Catalan triangle numbers and binomial coefficients, Contemp. Math. 713 (2018), 165-185.

  40. Jang Soo Kim, Kyu-Hwan Lee, and Se-jin Oh, Dominant maximal weights of highest weight modules and Young tableaux, Sém. Lothar. Combin. 78B (2017), Art. 25.

  41. Seok-Jin Kang, Kyu-Hwan Lee and Kyungyong Lee, A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras, Comm. Algebra. 45 (2017), no.11, 4785-4800.

  42. Lisa Carbone, Kyu-Hwan Lee and Dongwen Liu, Eisenstein series on rank 2 hyperbolic Kac-Moody groups, Math. Ann. 367 (2017), 1173-1197.

  43. Seok-Jin Kang, Kyu-Hwan Lee, Hansol Ryu and Ben Salisbury, A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1), Proc. Sympos. Pure Math. 92 (2016), 145-165.

  44. Konstantina Christodoulopoulou and Kyu-Hwan Lee, Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras, J. Pure Appl. Algebra 220 (2016), 3733-3751.

  45. Gabriel Feinberg and Kyu-Hwan Lee, Homogeneous representations of type A KLR-algebras and Dyck paths, Sém. Lothar. Combin. 75 (2016), Art. B75b.

  46. Henry H. Kim, Kyu-Hwan Lee and Yichao Zhang, Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras, Trans. Amer. Math. Soc. 367 (2015), no. 12, 8843-8860.

  47. Gabriel Feinberg and Kyu-Hwan Lee, Fully commutative elements of type D and homogeneous representations of KLR-algebras, J. Comb. 6 (2015), no. 4, 535-557.

  48. Kyu-Hwan Lee and Yichao Zhang, Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems, Trans. Amer. Math. Soc. 367 (2015), 597-625.

  49. Lisa Carbone, Walter Freyn and Kyu-Hwan Lee, Dimensions of imaginary root spaces of hyperbolic Kac-Moody algebras, Contemp. Math. 623 (2014), 23-40.

  50. Kyu-Hwan Lee, Philip Lombardo and Ben Salisbury, Combinatorics of the Casselman-Shalika formula in type A, Proc. Amer. Math. Soc. 142 (2014), 2291-2301.

  51. Henry H. Kim and Kyu-Hwan Lee, Rank 2 symmetric hyperbolic Kac-Moody algebras and Hilbert modular forms, J. Algebra 407 (2014), 81-104.

  52. Kyu-Hwan Lee and Ben Salisbury, Young tableaux, canonical bases and the Gindikin-Karpelevich formula, J. Korean Math. Soc. 51 (2014), no. 2, 289-309.

  53. Kyu-Hwan Lee and Philip Lombardo, Eisenstein series on affine Kac-Moody groups over function fields, Trans. Amer. Math. Soc. 366 (2014), no. 4, 2121-2165.

  54. Henry H. Kim and Kyu-Hwan Lee, Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms, Ramanujan J. 32 (2013), 329-352.

  55. Henry H. Kim and Kyu-Hwan Lee, Automorphic correction of the hyperbolic Kac-Moody algebra E10, J. Math. Phys. 54 (2013), 091701, 13 pp.

  56. Henry H. Kim and Kyu-Hwan Lee, A family of generalized Kac-Moody algebras and deformation of modular forms, Int. J. Number Theory 8 (2012), no. 5, 1107-1131.

  57. Henry H. Kim and Kyu-Hwan Lee, Quantum affine algebras, canonical bases and q-deformation of arithmetical functions, Pacific J. Math. 255 (2012), no. 2, 393-415.

  58. Kyu-Hwan Lee and Ben Salisbury, A combinatorial description of the Gindikin-Karpelevich formula in type A, J. Combin. Theory Ser. A 119 (2012), 1081-1094.

  59. Jonathan D. Axtell and Kyu-Hwan Lee, Vertex operator algebras associated to type G affine Lie algebras, J. Algebra 337 (2011), 195-223.

  60. Henry H. Kim and Kyu-Hwan Lee, Representation theory of p-adic groups and canonical bases, Adv. Math. 227 (2011), no. 2, 945-961.

  61. Kyu-Hwan Lee, Iwahori-Hecke algebras of SL_2 over 2-dimensional local fields, Canad. J. Math. 62 (2010), no. 6, 1310-1324.

  62. Seok-Jin Kang, Dong-il. Lee, Kyu-Hwan Lee and Hyungju Park, Linear algebraic approach to Gröbner-Shirshov basis theory, J. Algebra 313 (2007), 988-1004.

  63. Georgia Benkart, Seok-Jin Kang and Kyu-Hwan Lee, On the center of two-parameter quantum groups, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 3, 445-472.

  64. Henry H. Kim and Kyu-Hwan Lee, Spherical Hecke algebras of SL_2 over 2-dimensional local fields, Amer. J. Math. 126 (2004), no. 6, 1381-1399.

  65. Seok-Jin Kang, In-Sok Lee, Kyu-Hwan Lee and Hyekyung Oh, Representations of Ariki-Koike algebras and Gröbner-Shirshov bases, Proc. London Math. Soc. (3) 89 (2004), 54-70.

  66. Kyu-Hwan Lee, Gröbner-Shirshov bases for representations of Lie algebras and Hecke algebras of type A, Proceedings of the Third International Algebra Conference (Tainan 2002), 115-128, Kluwer Academic Publishers, Dordrecht, 2003.

  67. Seok-Jin Kang, In-Sok Lee, Kyu-Hwan Lee and Hyekyung Oh, Hecke algebras, Specht modules and Gröbner-Shirshov bases, J. Algebra 252 (2002), 258-292.

  68. Seok-Jin Kang and Kyu-Hwan Lee, Gröbner-Shirshov bases for irreducible sl_{n+1}-modules, J. Algebra 232 (2000), 1-20.

  69. Seok-Jin Kang and Kyu-Hwan Lee, Gröbner-Shirshov bases for representation theory, J. Korean Math. Soc. 37 (2000), 55-72.

  70. Leonid A. Bokut, Seok-Jin Kang, Kyu-Hwan Lee and Peter Malcolmson, Gröbner-Shirshov bases for Lie superalgebras and their universal enveloping algebras, J. Algebra 217 (1999), 461-495.

 
 
 

  publications -- machine learning for mathematics


  
 
 

  publications -- representation theory


  
 
 

  publications -- number theory


  
 
 

  publications -- combinatorics


  
 
 

  publications -- mathematical physics


  
 
 

  publications -- complex geometry


  
 
 

  non-submitted preprints


  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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