B.S. Mathematics (1993~1997) Korea Advanced Institute of Science and Technology (KAIST), Korea
M.S. Mathematics (1997~1999) Korea Advanced Institute of Science and Technology (KAIST), Korea
Ph.D. Applied Mathematics (1999~2004) Korea Advanced Institute of Science and Technology (KAIST), Korea
Work Experience
1. Professor at Seoul National University, Seoul (03/2020 ~ present)
2. Assistant/Associate Professor at Seoul National University, Seoul (03/2013 ~ 02/2020)
3. Assistant Professor at Chungbuk National University, Cheongju (03/2009 ~ 02/2013)
4. Postdoctral Fellow at University of Waterloo, Waterloo, Canada (07/2007 ~ 02/2009)
5. Research Assistant Professor at POSTECH, Pohang (02/2007 ~ 07/2007)
6. Visiting Scholar at TAMU, College Station, USA (10/2006 ~ 12/2006)
7. Visiting Postdoc (supported by KOSEF) at UIUC, Urbana-Champaign, USA (11/2005 ~ 10/2006)
8. BK21 Postdoc at Seoul National University, Seoul (03/2004 ~ 11/2005)
Research
Interests
Abstract harmonic analysis, Non-commutative probability, Non-commutative Lp spaces, Operator spaces, Quantum Information theory and Topological quantum groups.
Publications by topics
Geometry of Banach spaces and Operator spaces
1. (with C. Choi) Operators of Fourier type p with respect to some subgroups of a locally compact abelian group. Arch. Math.(Basel) 81 (2003), No.4, 457-466.
10. (with Ebrahim Samei and Matthew Wiersma) New tensor products of C*-algebras and characterization of type I C*-algebras as rigidly symmetric C*-algebras. Trans. Amer. Math. Soc. 377, Number 6 (2024), 4223?4253.
2. (with E. Ricard) Hypercontractivity on the q-Araki-Woods algebras. Comm. Math. Phys, 305(2) (2011), 533-553.
3. (with N. Obata) Distance-k graphs of hypercube and q-Hermite polynomials. Infin. Dimens. Anal. Quantum Probab. Relat. Top.,
Vol. 16, No. 2 (2013) 1350011 (12 pages).
4. (with Y. Hibino and N. Obata) Asymptotic Spectral Distributions of Distance k-Graphs of Cartesian Product Graphs, Colloq. Math. 132 (2013), 35-51.
Abstract harmonic analysis on groups
1. (with B. E. Forrest and E. Samei) Projectivity of modules over Fourier algebras. Proc. London Math. Soc. (2011) 102(4): 697-730.
2. (with E. Samei) Beurling-Fourier Algebras, operator amenability and Arens Regularity. J. Funct. Anal. 262 (2012), 167-209.
3. (with B. E. Forrest and E. Samei) Projectivity of modules over Segal algebras. Houston J. Math. Volume 39, No. 2 (2013) 531-560.
4. (with B. Collins and P. Sniady) Dimensions of components of tensor products of the linear groups representations, Studia Math. 220 (2014), 221-241.
5. (with E. Samei and N. Spronk) Some weighted group algebras are operator algebras. Proc. Edinburgh Math. Soc., Volume 58 / Issue 02 / June 2015, pp 499-519.
6. (with M. Ghandehari, E. Samei and N. Spronk) Some Beurling-Fourier algebras are operator algebras. Trans. Amer. Math. Soc. 367, Number 10 (2015), 7029-7059.
7. (with J. Ludwig, E. Samei and N. Spronk) Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math. 292 (2016), 11-41.
8. (with E. Samei and N. Spronk)
Similarity degree of Fourier algebras, J. Funct. Anal. 271 (2016), 593-609.
9. (with S.-G. Youn) New deformations of Convolution algebras and Fourier algebras on locally compact groups, Canad. J. Math. 69 (2017), 434-452.
10. (with E. Samei and N. Spronk) p-Fourier algebras on compact groups, Revista Matematica Iberoamericana, Volume 34, Issue 4 (2018) 1469-1514.
11. (with E. Samei and N. Spronk)
Corrigendum: Similarity degree of Fourier algebras, J. Funct. Anal. Volume 277, Issue 3 (2019) 958-964.
12. (with M. Ghandehari, J. Ludwig, N. Spronk and L. Turowska)
Beurling-Fourier algebras on Lie groups and their spectra, to appear in Adv. Math. arXiv:1808.05914.
14. (with Heon Lee)
Analytic subalgebras of Beurling-Fourier algebras and complexification of Lie groups, preprint arXiv:2401.03763.
Abstract harmonic analysis on quantum groups
1. (with M. Caspers and E. Ricard) Operator biflatness of the L^1-algebras of compact quantum groups, J. Reine Angew. Math. (Crelle's Journal) Volume 2015, Issue 700, Pages 235-244.
2. (with U. Franz and A. Skalski)
Integration over the quantum diagonal subgroup and associated Fourier-like algebras, Int. J. Math. Vol. 27, No. 09, 1650073 (2016).
3. (with U. Franz) Beurling-Fourier algebras of compact quantum groups: characters and finite dimensional representations, Indiana Univ. Math. J. 70 No. 2 (2021), 605--637.
Quantum information theory
1. (with M. Brannan, B. Collins and S.-G. Youn)
Temperley-Lieb quantum channels, Comm. Math. Phys., volume 376, pages 795--839 (2020).
2. (with C. Beny and S. J. Park)
Twisted Fourier analysis and pseudo-probability distributions, preprint, arXiv:2004.13860.
3. (with S.-G. Youn)
Quantum channels with quantum group symmetry, Comm. Math. Phys., volume 389, pages 1303?-1329 (2022).
4. (with E. Chang, J. Kim, H. Kwak, and S.-G. Youn) Irreducibly SU(2)-covariant quantum channels of low rank. Reviews in Mathematical Physics, Vol. 34, No. 07, 2250021 (2022)
Honours
TJ Park Junior Faculty Fellowship, POSCO TJ Park Foundation, 2012.
2012 Basic research outstanding achivements (50 selected) supported by ministry of education, science and technology, Korea.
2016 Brain Pool program (KOFST) outstanding achivements, KOFST, 2017.
2018 Research awards, College of Natural Sciences, Seoul National University.
Former PhD students
Sang-Gyun Youn
(Assistant professor, Department of Mathematics Education, SNU)
Former Postdoc
Xiao Xiong
(Professor at Harbin Institute of Technology, Harbin, China)
Editorship
Editor, Journal of the Korean Mathematical Society (2015 ~ 2023)
Funded Projects
Non-commutative Lp-theory in abstract harmonic analysis
1/5/2009 - 30/4/2012
NRF (Çѱ¹¿¬±¸Àç´Ü)
Non-commutative extensions of harmonic analysis
1/5/2012 - 30/4/2015
NRF (Çѱ¹¿¬±¸Àç´Ü)
Analysis on locally compact groups via Fourier algebras and its quantum extension
1/5/2015 - 30/4/2018
NRF (Çѱ¹¿¬±¸Àç´Ü)
Functional analytic approach to quantum channel capacities