Center for Mathematical Challenges
Kim, Sang-hyun
Professor
Geometric Group Theory
Sang-hyun Kim works on geometric group theory and low-dimensional topology. His research interests include right-angled Artin groups, mapping class groups and word-hyperbolic groups. With the collaborators, he developed topological and analytic methods to attack embeddability problems between groups of geometric nature. These groups encompass surface groups, manifold diffeomorphism groups and finitely generated groups of specifically prescribed smoothness.
- Yale University, Ph.D., 2007. (Advisor : Andrew Casson)
- Postdoctoral Fellow, Mathematical Sciences Research Institute (MSRI), 2007.
- R. H. Bing Instructor, the University of Texas at Austin, 2008 - 2010.
- Norbert Wiener Assistant Professor, Tufts University, 2010 - 2011.
- Assistant / Associate Professor, KAIST, 2010 - 2014.
- Associate Professor, Department of Mathematical Sciences, Seoul National University, 2014 - 2019.
- Professor, KIAS, 2019 - present.
- R. H. Bing Fellowship, the University of Texas at Austin, 2008 - 2010.
- Sang-San Prize for Young Mathematicians, Korean Mathematical Society, 2012.
- Creative Teaching Grand Award, KAIST, 2013.
- Teaching Excellence Award, College of Natural Sciences, Seoul National University, 2015.
- Excellent Paper Award, Korean Mathematical Society, 2016.
- Research Excellence Award, College of Natural Sciences, Seoul National University, 2017.
- Y-KAST member (Young Korean Academy of Science and Technology), 2018 - present.
Publications at KIAS
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Virtual Critical Regularity of Mapping Class Group Actions on the Circle
TRANSFORMATION GROUPS, 2024 -
Non-freeness of Groups Generated by Two Parabolic Elements with Small Rational Parameters
MICHIGAN MATHEMATICAL JOURNAL, 2022 -
Shapes of hyperbolic triangles and once-punctured torus groups
MATHEMATISCHE ZEITSCHRIFT, 2021 -
DIRECT PRODUCTS, OVERLAPPING ACTIONS, AND CRITICAL REGULARITY
JOURNAL OF MODERN DYNAMICS, 2021 -
Small C-1 actions of semidirect products on compact manifolds
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2020 -
INTEGRABILITY OF MODULI AND REGULARITY OF DENJOY COUNTEREXAMPLES
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020 -
Diffeomorphism groups of critical regularity
INVENTIONES MATHEMATICAE, 2020 -
Flexibility of Group Actions on the Circle Introduction
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Flexibility of Group Actions on the Circle Preface
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Preliminaries
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Topological Baumslag Lemmas
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Splittable Fuchsian Groups
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Combination Theorem for Flexible Groups
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Axiomatics
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Mapping Class Groups
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Zero Rotation Spectrum and Teichmuller Theory
FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE, 2019 -
Unsmoothable group actions on compact one-manifolds
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019 -
CHAIN GROUPS OF HOMEOMORPHISMS OF THE INTERVAL
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2019
Selected Publications
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Diffeomorphism groups of critical regularity
Inventiones mathematicae, 221(2), 421-501 (2020). -
Embeddability between right-angled Artin groups
Geometry & Topology 17 (2013) 493-530. -
Anti-trees and right-angled Artin subgroups of braid groups
Geometry & Topology 19-6 (2015), 3289-3306. -
Unsmoothable group actions on compact one-manifolds
Journal of European Mathematical Society, Volume 21, Issue 8, 2019, pp. 2333–2353. -
Chain groups of homeomorphisms of the interval and the circle
Annales Scientifiques de l'École Normale Supérieure, Series 4, Volume (52), 2019, 797-820. -
Structure and regularity of group actions on one-manifolds
285 pages, Springer Monographs in Mathematics (November 21, 2021). -
Free products and algebraic structures of diffeomorphism groups
Journal of Topology, Volume11, Issue4, December 2018, Pages 1053-1075. -
Coxeter groups, hyperbolic cubes, and acute triangulations
Journal of Topology (2016) 9 (1): 117-142 -
Hyperbolic Surface subgroups of one-ended doubles of free groups
Journal of Topology (2014) 7 (4): 927-947. -
Lagrangian Floer potential of orbifold spheres
Advances in Mathematics, Volume 306, 14 January 2017, Pages 344-426.
- Office: 1540 / /
- Center for Mathematical Challenges, Korea Institute for Advanced Study
- 85 Hoegiro Dongdaemun-gu, Seoul 02455, Republic of Korea.