Kim, Hyun Kyu
Professor
Physical Mathematics
Hyun Kyu Kim works on topics related to Physical Mathematics, especially the quantum aspects of geometry and topology of low dimensional manifolds. Specifically, his research topics include Teichmüller spaces and higher Teichmüller spaces of surfaces, their cluster variety structures and quantization thereof, skein algebras, as well as three dimensional quantum gravity.
2008.05: Bachelor of Arts in Mathematics, Cornell University
2011.12: M.Phil. and M.S. in Mathematics, Yale University
2013.05: Ph.D. in Mathematics, Yale University (thesis advisor: Igor B. Frenkel)
2013.06 - 2016.06: Research Fellow, Korea Institute for Advanced Study, School of Mathematics
2016.06 - 2017.02: KIAS Assistant Professor, Korea Institute for Advanced Study, School of Mathematics
2017.03 - 2022.02: Assistant Professor, Ewha Womans University, Department of Mathematics
2022.02 - 2022.08: Associate Professor, Ewha Womans University, Department of Mathematics
2022.09 - 2023.08: KIAS Fellow (KIAS Associate Professor), Korea Institute for Advanced Study, School of Mathematics
2023.09 - present: Professor, Korea Institute for Advanced Study, School of Mathematics
2016: Sangsan prize for Young Mathematicians, Korean Mathematical Society
Publications at KIAS
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A Quantization of Moduli Spaces of 3-Dimensional Gravity
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2024 -
Three-Dimensional Quantum Gravity from the Quantum Pseudo-Kahler Plane
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2023 -
SL2 quantum trace in quantum Teichm?ller theory via writhe
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2023 -
Quasiphantom categories on a family of surfaces isogenous to a higher product
JOURNAL OF ALGEBRA, 2017 -
A duality map for quantum cluster varieties from surfaces
ADVANCES IN MATHEMATICS, 2017 -
The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
ADVANCES IN MATHEMATICS, 2016 -
Ratio coordinates for higher Teichmuller spaces
MATHEMATISCHE ZEITSCHRIFT, 2016
Selected Publications
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SL3-laminations as bases for PGL3 cluster varieties for surfaces
Memoirs of the American Mathematical Society, 게재예정 -
Quantum Teichmüller space from the quantum plane
Duke Mathematical Journal, 161(2), 305-366 -
A duality map for quantum cluster varieties from surfaces
Advances in Mathematics, 306, 1164-1208 -
A quantization of moduli spaces of 3-dimensional gravity
Communications in Mathematical Physics, 405, article 144 (online) -
Laurent positivity of quantized canonical bases for quantum cluster varieties from surfaces
Communications in Mathematical Physics, 373(2), 655-705, arXiv:1710.06217 -
The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
Advances in Mathematics, 293, 529-588 -
SL2 quantum trace in quantum Teichmüller theory via writhe
Algebraic & Geometric Topology, 23(1), 339-418, -
Naturality of SL3 quantum trace maps for surfaces
Quantum Topology 게재예정 -
Three dimensional construction of the Virasoro-Bott group
preprint
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