The main objects of study of Hyun Kyu Kim are various mathematical objects arising from Mathematical Physics. He has been focusing especially on the problem of quantization of moduli spaces of geometric structures on manifolds. Various areas of mathematics are involved in this problem, such as Differential Geometry, Riemannian Geometry, Algebraic Geometry, Topology, Representation Theory, Functional Analysis, Harmonic Analysis and Combinatorics. The research topics and previous works of Kim span over these areas. Kim's major accomplishments are about Quantum Teichmüller Theory (which is related to quantization of 2 dimensional geometry), and about quantization of higher Teichmüller spaces and cluster varieties. Recent works, including joint works with students at Ewha, mostly lie in the area of Geometric Topology. Besides, Kim has been working on other various topics like representation theory of quantum groups, representation theory of finite simple groups, algebraic geometry related to algebraic surfaces, and universal Teichmüller spaces.
- Research Interests
- Geometric Topology, Mathematical Physics, Quantum Geometry, Representation Theory, Group Theory
Research Record
- Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants Journal of Geometry and Physics, 2021 , 104103
- Phase constants in the Fock–Goncharov quantum cluster varieties Analysis and Mathematical Physics, 2021, v.11 no.1, 2
- Comments on Exchange Graphs in Cluster Algebras Experimental Mathematics, 2020, v.29 no.1, 79-100
- Laurent Positivity of Quantized Canonical Bases for Quantum Cluster Varieties from Surfaces Communications in Mathematical Physics, 2020, v.373 no.2, 655-705
- Finite dimensional quantum Teichmüller space from the quantum torus at root of unity Journal of Pure and Applied Algebra, 2019, v.223 no.3, 1337-1381
- A duality map for quantum cluster varieties from surfaces ADVANCES IN MATHEMATICS, 2017, v.306, 1164-1208
- Quasiphantom categories on a family of surfaces isogenous to a higher product JOURNAL OF ALGEBRA, 2017, v.473, 591-606
- Ratio coordinates for higher Teichmuller spaces MATHEMATISCHE ZEITSCHRIFT, 2016, v.283 no.1-2, 469-513
- The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization ADVANCES IN MATHEMATICS, 2016, v.293, 529-588
- [학술지논문] Phase constants in the Fock-Goncharov quantum cluster varieties ANALYSIS AND MATHEMATICAL PHYSICS, 2021, v.11 no.1 , 1-66
- [학술지논문] Comments on Exchange Graphs in Cluster Algebras EXPERIMENTAL MATHEMATICS, 2020, v.29 no.1 , 79-100
- [학술지논문] Laurent Positivity of Quantized Canonical Bases for Quantum Cluster Varieties from Surfaces COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, v.373 no.2 , 655-705
- [학술지논문] Finite dimensional quantum Teichmuller space from the quantum torus at root of unity JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, v.223 no.3 , 1337-1381
- [학술지논문] A duality map for quantum cluster varieties from surfaces ADVANCES IN MATHEMATICS, 2017, v.306 no.1 , 1164-1208
- [학술지논문] Quasiphantom categories on a family of surfaces isogenous to a higher product JOURNAL OF ALGEBRA, 2017, v.473 no.1 , 591-606
- [학술지논문] Ratio coordinates for higher Teichmuller spaces MATHEMATISCHE ZEITSCHRIFT, 2016, v.283 no.1-2 , 469-513
- [학술지논문] The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization ADVANCES IN MATHEMATICS, 2016, v.293 no.1 , 529-588
- [학술지논문] QUANTUM TEICHMULLER SPACE FROM THE QUANTUM PLANE DUKE MATHEMATICAL JOURNAL, 2012, v.161 no.2 , 305-366
- [저역서] 다변수 미분적분학 경문사(경문북스), 2020, 184
- [학술발표] Quantum Teichmüller theory 2017년도 대한수학회 봄 연구발표회, 대한민국, 광주, 2017-04-29 2017년도 대한수학회 봄 연구발표회 Program/Abstracts, 2017, 48-48
Courses
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2022-1st
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Topology I
- Subject No 20449Class No 01
- 3Year ( 3Credit , 3Hour) Tue 2~2 (POSCO366) , Fri 3~3 (POSCO366)
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Differential Topology
- Subject No G10472Class No 01
- Year ( 3Credit , 3Hour) Wed 2~3 (-)
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2021-2nd
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Calculus II
- Subject No 20408Class No 01
- 1Year ( 3Credit , 3Hour) Mon 3~3 , Wed 2~2
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Algebraic Topology
- Subject No G10744Class No 01
- Year ( 3Credit , 3Hour) Fri 2~3 (D106)
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2021-1st
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Differential Geometry I
- Subject No 20433Class No 01
- 4Year ( 3Credit , 3Hour) Tue 4~4 , Fri 5~5
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Multivariable Calculus 강의 계획서 상세보기
- Subject No 38188Class No 01
- 2Year ( 3Credit , 3Hour) Wed 3~3 , Fri 2~2
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Academic Background
Yale University Ph.D.(Mathematics)
Yale University Master of Science(Mathematics)
Yale University Master of Philosophy(Mathematics)
Cornell University B.A.(Mathematics)