- Operator Algebra
- Topological Quantum Group
- Non-commutative Harmonic Analysis
- Quantum Information Theory
- Random Matrix Theory and Free Probability
- Mathematics Education
Publications
Mathematics and Mathematical applications
20. Twisted Fourier transforms on non-Kac compact quantum groups. arXiv:2503.23316.
19. An analytic characterization of freeness for finitely generated discrete quantum groups. arXiv:2411.11043. (with Yoonje Jeong)
18. A Khintchine inequality for central Fourier series on non-Kac compact quantum groups. arXiv:2408.13519.
17. A central limit theorem for partial transposes of multipartite Wishart matrices, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics, arXiv:2405.02822. (with Gyunam Park)
16. k-positivity and Schmidt number under orthogonal group symmetries. Quantum Information Processing, 23, 162 (2024). (with Sang-Jun Park)
15. A universal framework for entanglement detection under group symmetry. Journal of Physics A: Mathematical and Theoretical, 57, 325304 (2024). (with Sang-Jun Park, Yeong-Gwang Jung, Jeongeun Park)
14. Gaussian quantum information over general quantum kinematical systems I: Gaussian states, Letters in Mathematical Physics, 115, 32 (2025). (with Cedric Beny, Jason Crann, Hun Hee Lee, Sang-Jun Park)
13. Strong Haagerup inequalities on non-Kac free orthogonal quantum groups. Journal of Functional Analysis, 283 (5), 109557 (2022).
12. Irreducibly SU(2)-covariant quantum channels of low rank. Reviews in Mathematical Physics, 34 (7), 2250021 (2022). (with Euijung Chang, Jaeyoung Kim, Hyesun Kwak, Hun Hee Lee)
11. Asymptotic analysis for $O_N^+$-Temperley-Lieb quantum channels. Quantum Information Processing, 20, 291 (2021).
10. Quantum channels with quantum group symmetry. Communications in Mathematical Physics, 389 (3): 1303-1329 (2022). (with Hun Hee Lee)
9. Property RD and hypercontractivity for orthogonal free quantum groups. International Mathematics Research Notices, 2021 (2): 1573-1601. (with Michael Brannan and Roland Vergnioux)
8. Additivity violation of the regularized minimum output entropy. Documenta Mathematica, 27 (2022),1299-1320. (with Benoît Collins)
7. On the Sobolev embedding properties for compact matrix quantum groups of Kac type. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3341-3366.
6. Temperley-Lieb quantum channels. Communications in Mathematical Physics, 376 (2): 795-839 (2020). (with Michael Brannan, Benoît Collins and Hun Hee Lee)
5. Entropic uncertainty relations under localizations on discrete quantum groups. Journal of Mathematical Physics, 59, 073501 (2018).
4. A theorem for random Fourier series on compact quantum groups. Indiana University Mathematics Journal, 69 (2020), 887-910.
3. On the similarity problem for locally compact quantum groups. Journal of Functional Analysis, 276 (2019), 1313-1337. (with Michael Brannan)
2. Hardy-Littlewood inequalities on compact quantum groups of Kac type. Analysis & PDE, 11-1: 237-261, 2018.
1. New deformations of convolution algebras and Fourier algebras on locally compact groups. Canadian Journal of Mathematics, 69(2): 434-452, 2017. (with Hun Hee Lee)
Mathematics Education
3. Pre-service Teachers’ Mathematical Content Knowledge and Perceptions on Justification of the Differentiation of the Exponential Function. Journal of Korea Society Educational Studies in Mathematics: School Mathematics, 2024, 26 (3): 363-385. (with J-W.Noh, M-J.Kim, M-J.Kim).
2. Development of creative problem-solving activities for integrating Mathematics and Information Science -Focusing on the hat game for mathematically gifted students. Journal of the Korean Society of Mathematical Education Series E: Communications of Mathematical Education, 2022, 36(3): 439-467. (with J. Seo)
1. On types of Justifications of $(e^x)'=e^x$ in Analysis Textbooks for Pre-service Teacher Education. Journal of Korea Society Educational Studies in Mathematics: School Mathematics, 2022, 24 (3): 387-411. (with G. Ryu and J-W. Noh)
96. Ewha Wamans University, September 2025
95. The 2nd China-Japan-Korea Conference on Functional Analysis: Seoul National University, July 2025
94. National Tsing Hua University, July 2025
93. The 26th Conference of the International Linear Algebra Society, June 2025
92. Queen's University, May 2025
91. KMS Spring Meeting: KAIST, April 2025
90. Quantum Group Seminar (Online), March 2025
89. Non-commutative probability, random matrices and Lévy processes, March 2025
88. Kyoto University, February 2025
87. NextQuantum Workshop, January 2025
86. Winter Camp for Functional Analysis: Chungbuk National University, January 2025
85. SNU-HU math symposium, November 2024
84. Analysis on Function Spaces, KMS Fall Meeting: Sungkyunkwan University, October 2024
83. Quantum Information and Quantum Computation, KMS Fall Meeting: Sungkyunkwan University, October 2024
82. The 1st China-Japan-Korea Conference on Functional Analysis: Harbin Institute of Technology, August 2024
81. Bielefeld-Melbourne-Seoul Random Matrix Seminar (Online), July 2024
80. International Congress On Mathematical Physics: Strasbourg, July 2024
79. Université de Toulouse, June 2024
78. National Institute for Mathematical Sciences (NIMS), May 2024
77. KMS Spring Meeting: Daejeon, April 2024
76. Noncommutative Geometry, Analysis on Groups, and Mathematical Physics (Online), March 2024
75. Winter Camp for Functional Analysis: Chungbuk National University, February 2024
74. Applied Topology Seminar: KAIST, February 2024
73. The 19th ILJU School of Mathematics: Postech, January 2024
72. Quantum Information Theory and Free Probability: New York University Abu Dhabi, January 2024
71. Winter School on Functional Analysis: December 2023
70. Analysis Seminar: Korea Institute for Advanced Study, November 2023
69. Annual Forum 2023: Samsung Science & Technology Foundation, November 2023
68. Joint seminar on quantum information theory with Université de Toulouse: Seoul National University, October 2023
67. Operator Algebras and Operator Theory Seminar: Seoul National University, October 2023
66. Operator Algebras and Operator Theory Seminar: Seoul National University, October 2023
65. Noncommutative Harmonic Analysis and Quantum Information: Mittag-Leffler Institute (Sweden), June 2023
64. Colloquium: Chungbuk National University, May 2023
63. KMS Spring Meeting: Daejeon, April 2023
62. The 43rd International Conference on Quantum Probability and Infinite Dimensional Analysis: Yeosu, January 2023
61. Analysis Seminar: Chung-Ang University, December 2022
60. Quantum Groups: Current Trends and New Perspectives: Workshop at University of Oslo (Norway), December 2022
59. Colloquium: University of Ulsan, November 2022
58. Operator Algebras and Operator Theory Seminar: Seoul National University, October 2022
57. Noncommutative harmonic analysis and quantum groups: Będlewo (Poland), September 2022
56. Analysis Seminar: University of Waterloo (Canada), September 2022
55. The 17th ILJU School of Mathematics: Postech, August 2022
54. Université de Toulouse, July 2022
53. Analysis Seminar: Hanyang University, June 2022
52. KMS Spring Meeting (Online), April 2022
51. Quantum Computation/Information/Cryptography Seminar: Seoul National University, November 2021
50. Operator algebra related topics, SNU-HU math symposium 2021 (Online), November 2021
49. Mathematics Colloquium: Seoul National University, November 2021
48. KMS Fall Meeting (Online), October 2021
47. Beyond IID in Information Theory 9 (Online), September 2021
46. Quantum Computation/Information/Cryptography Seminar: Seoul National University, September 2021
45. 수인학회 (Online), August 2021
44. Operator Algebras in Quantum Theory, International Workshop on Operator Theory and its Applications (Online), August 2021
43. Quantum Groups and Algebraic Quantum Field Theory, International Workshop on Operator Theory and its Applications (Online), August 2021
42. CMS Summer Meeting (Online), June 2021
41. KMS Spring Meeting (Online), April 2021
40. QST Seminar (Online), February 2021
39. Operator algebra related topics, SNU-HU math symposium 2020 (Online), November 2020
38. Operator Algebras and Operator Theory Seminar: Seoul National University, September 2020
37. The 18th Korea Operator Algebra Seminar: Pyeongchang , August 2020
36. KMS Spring Meeting (online), July 2020
35. Quantum Computation/Information/Cryptography Seminar: Seoul National University, May 2020
34. Quantum Computation/Information/Cryptography Seminar: Seoul National University, March 2020
33. Quantum Computation/Information/Cryptography Seminar: Seoul National University, March 2020
32. Linear Analysis Seminar: Texas A&M, January 2020
31. Analysis Seminar: University of Houston, January 2020
30. Seminar on Free Probability and Random Matrices: Queen's University, December 2019 (2 lectures)
29. Analysis Seminar: University of Ottawa, October 2019
28. Quantum Information Seminar: Korea Institute for Advanced Study, July 2019
27. KOTAC 2019: Gyeongju, June 2019
26. Analysis Seminar: Chonnam National University, June 2019
25. Analysis Seminar: Hanyang University, June 2019
24. Analysis Seminar: Korea Institute for Advanced Study, June 2019
23. Random Matrix Seminar: KAIST, June 2019
22. Mathematical Aspects in Current Quantum Information Theory 2019: Seoul National University, May 2019
21. The 2nd Quantum computation and Information Workshop: Texas A&M University, May 2019
20. Seminar on Free Probability and Random Matrices: Queen's University, April-May 2019 (3 lectures)
19. Analysis Seminar: Carleton University, February 2019
18. Analysis Seminar: University of Waterloo, February 2019
17. CMS Winter Meeting: Vancouver, December 2018
16. Joint Meeting of KMS and DMV: Seoul, October 2018
15. Kyoto Operator Algebra Seminar: Kyoto University, September 2018
14. The 14th Korea Operator Algebra Seminar: Busan, June 2018
13. Analysis Seminar: Hanyang University, May 2018
12. KMS Spring Meeting: Kyung Hee University, April 2018
11. Operator Algebras and Operator Theory Seminar: Seoul National University, March 2018
10. Operator Algebras and Operator Theory Seminar: Seoul National University, November 2017
9. Topological quantum groups and harmonic analysis: Seoul National University, May 2017
8. KMS Spring Meeting: Chosun University, April 2017
7. Analysis Seminar: Baylor University, November 2016
6. Analysis Seminar: University of Houston, November 2016
5. Linear Analysis Seminar: Texas A&M University, September 2016
4. Operator Algebras and Operator Theory Seminar: Seoul National University, September 2016
3. Operator Algebras and Operator Theory Seminar: Seoul National University, March 2016
2. Operator Algebras and Operator Theory Seminar: Seoul National University, December 2015
1. KMS Fall Meeting: Yonsei University, October 2015
Slides
Fourier analysis on compact groups: https://drive.google.com/file/d/1vsHVOPZxILJF1gPIXMfAov0MZW-dGoS6/view?usp=share_link
Additivity violation of the regularized minimum output entropy in the commuting operator framework: https://drive.google.com/file/d/1N3xDuSJOmmHGSDFXeH8sqQu_toD_Q_x3/view?usp=share_link
(Strong) Haagerup inequalities on free orthogonal quantum groups: https://drive.google.com/file/d/1y9ZDkILlJYUkBore7D4iApcW1tyBoveq/view?usp=share_link
Information-theoretic analysis of SU(2)-covariant quantum channels: https://drive.google.com/file/d/1UKBIWtozT2b_cjDrPZf8uoEz--jJczt7/view?usp=share_link
Random matrices and operator algebras: https://drive.google.com/file/d/1kayVqGA3diW-4mcWDlDRQlYIbLSICZnn/view?usp=share_link
Shannon information theory: https://drive.google.com/file/d/19--beAbQoxWe3IRJqbIaaQXSyEateLQO/view?usp=share_link
Basics of quantum information theory: https://drive.google.com/file/d/18VYyFhtiJFwpO7pdlviyq4V9KKpv8wOc/view?usp=share_link
Additivity questions in quantum information theory: https://drive.google.com/file/d/15HNYZRVVNiKf75w8B8dtjxgW7zQHl65q/view?usp=share_link
Sobolev embedding properties on compact Lie groups and duals of discrete groups : https://drive.google.com/file/d/16V2qGpDVMkGbmhFwjMiXkK-yQsRuIOPs/view?usp=share_link
Sobolev embedding properties on compact quantum groups: https://drive.google.com/file/d/1z1sJktC3JukMtXug3lXkrbZclbzPK7wa/view?usp=share_link
A majorization theorem by Lieb and Solovej for Temperley-Lieb quantum channels with the lowest weights: https://drive.google.com/file/d/1OOyWYbyL0Pm6We-ZSHMiNIPGmRi0bsAT/view?usp=share_link
Similarity problem for locally compact quantum groups: https://drive.google.com/file/d/1fU_GV8_GFg1eh2LDu1NwBJWnI6kYjWzl/view?usp=share_link
Random matrix techniques in quantum information theory: https://drive.google.com/file/d/1KP3H1hQ8xsFxotr-z2p24FL-5PB6wdxD/view?usp=share_link
Temperley-Lieb quantum channels: https://drive.google.com/file/d/1hBueEGNDM6nECrjsWOelfSVjaFjuX9Mu/view?usp=share_link
Entropic uncertainty principles on topological quantum groups: https://drive.google.com/file/d/1E_ZibmnF_t6ryGbXb2WxOe-f5Zz33wGu/view?usp=share_link
Complete representability problem for convolution algebras of locally compact quantum groups: https://drive.google.com/file/d/1bLPR9QZkcVOLEIq8PjcdWwo3vxX89oG_/view?usp=share_link
Non-commutative Khintchine inequalities and their applications to multipliers from Lp into lq: https://drive.google.com/file/d/1bLPR9QZkcVOLEIq8PjcdWwo3vxX89oG_/view?usp=share_link
Hardy-Littlewood inequalities on compact quantum groups of Kac type: https://drive.google.com/file/d/1xAAn4RNdaYep1f-AsgE4HSz1WHXkgOJe/view?usp=share_link