Sang-hyun Kim

Geometric Group Theory & Low-dimensional Topology

I am Professor and Chair in the School of Mathematics at Korea Institute for Advanced Study (KIAS). I also hold an affiliate professorship at the Graduate School of AI for Math, KAIST. Before joining KIAS in 2019, I worked at Seoul National University, KAIST, Tufts University, the University of Texas at Austin and MSRI. I received a Ph.D in 2007 at Yale University under the supervision of Andrew Casson.

My research interests focus on the interplay between geometric group theory and low-dimensional topology, particularly motivated by right-angled Artin groups and manifold diffeomorphism groups. I was selected as the Scientist of the Month (July 2020) by the Korean Ministry of Science and ICT.

Email: kimsh@kias.re.kr / skim.math@gmail.com
Seminar: visgat.kimsh.kr
CV: Download (Current)

Profiles: arXiv MathSciNet ORCiD KIAS

Education Projects

edu.kimsh.kr — A Math Demonstration Project

New Events (2026)

Casson Memorial, 2027, Yale University, US
Young Geometric Group Theory (yGGT) XIV, June 8 - 12, 2026, KIAS, Korea
Current Challenges in Topology, Samsung Global Symposium, Milan, Italy, May 21-23, 2026

Selected Work

First order rigidity of homeomorphism groups of manifolds (With Thomas Koberda and Javier de la Nuez-Gonzalez) Comm. Amer. Math. Soc. 5 (2025), 144-194.
[ArXiv] [Journal]

▶ Abstract

We prove that every compacted connected manifold M admits a purely group theoretic first order sentence "I-am-M" in its homeomorphism group, and also in its measure-preserving homeomorphism group. Consequently, these groups are first order rigid among the (measure-preserving) homeomorphism groups of compact connected manifolds.
Diffeomorphism groups of critical regularity (With Thomas Koberda) Inventiones mathematicae (2020)
[PDF] [Journal]

▶ Abstract

We prove that for each real numbers a ≥ 1, there exists a finitely generated subgroup G a of Diff a (S 1 ) with the property that G a admits no injective homomorphisms into Diff b (S 1 ) for all b > a. We also prove that there exists another fg group H a that embeds into Diff b (S 1 ) for all b < a, but not into Diff a (S 1 ). One can further require the same properties are inherited to all finite index subgroups and to the commutator groups of G a and of H a . The commutator groups will be simple.
Chain groups of homeomorphisms of the interval and the circle (With Thomas Koberda and Yash Lodha) Annales Scientifiques de l'École Normale Supérieure (2019)
[PDF] [Link]

▶ Abstract

We study subgroups of Homeo(R) generated by finitely many homeomorphisms each of which is supported on a single interval. As a consequence, we construct uncountably many non-pairwise isomorphic countable simple orderable groups.
Unsmoothable group actions on compact one-manifolds (With Hyungryul Baik and Thomas Koberda) Journal of European Mathematical Society (2019)
[ArXiv] [Link]

▶ Abstract

Let G be the mapping class group of a surface (possibly with punctures or boundary), such that G is not virtually free. We prove that G never admits, even virtually, an embedding into the C 1+bv diffeomorphism group of the circle.
Coxeter groups, hyperbolic cubes, and acute triangulations (With Genevieve Walsh) Journal of Topology (2016)
[PDF] [Link]

▶ Abstract

We prove that a combinatorial triangulation L of S 2 can be realized as an acute geodesic triangulation if and only if L does not have a separating three- or four-cycle.
Embedability between right-angled Artin groups (With Thomas Koberda) Geometry & Topology (2013)
[PDF] [Link]

▶ Abstract

We propose that a notion of ``extension graph'' can be used for a systematic study of embedability between two RAAGs.

Distinction

The Choi Seok-jeong Award, Korean Ministry of Science and ICT, November 2023. [News] [Ceremony]
The Scientist and Engineer of the Month, Korean Ministry of Science and ICT, July 2020.
Y-KAST Member, Korean Academy of Science and Technology (KAST), Feb 26, 2018 - present.
Research Excellence Award, College of Natural Sciences, Seoul National University, March 3, 2017.
Excellent Paper Award, Korean Mathematical Society, April 23, 2016.
For the work: (With Thomas Koberda), Embedability between right-angled Artin groups, Geometry & Topology 17 (2013) 493--530.
Teaching Excellence Award, College of Natural Sciences, Seoul National University, September 15, 2015.
Creative Teaching Grand Award, KAIST, February 15, 2013.
Sang-San Prize for Young Mathematicians, Korean Mathematical Society, October 5, 2012.
Silver medal, the 34th International Mathematical Olympiad, Turkey, 1993.