My research interests can be labeled by `Quantum Geometry', `Quantum Topology', `Geometric Topology', `Quantum Algebra', `Representation Theory' and `Physical Mathematics' (`Mathematical Physics' in Korea seems to be restricted only to PDE related topics).

More specifically, I'm interested in:

• quantization of (higher) Teichmüller space of a non-compact (Riemann) surface

• representation theory of quantum groups, infinite dimensional Lie algebras, mapping class groups, and the (braided) Ptolemy-Thompson groups

• the universal Teichmüller space and its quantization

• (2+1)-gravity theory and its quantization in Physics: especially Chern-Simons theory (in 3-dim)

• relationship between 2d (complex and hyperbolic) geometry and 3d (AdS) geometry

• diffeomorphism groups of spheres and balls

• cluster varieties and their quantization

• (SL2, SL3 and SLn) skein algebras

• quantized K-theoretic Coulomb branch (for 4d N=2 field theories of class S)

• categorification of skein algebras

• nice vector space bases (such as canonical basis, theta basis, etc) for quantum cluster algebras and skein algebras

• modular functor conjecture (especially the SL2 case, related to the Liouville conformal field theory)

• uniform construction of finite simple groups

My office is 1229 KIAS, Seoul, Korea. (since September 2023)

KIAS: http://www.kias.re.kr/

I'm trying to run: Geometry, Algebra and Physics (GAP) Seminar at KIAS

I'm an editor of

• Journal of the Korean Mathematical Society 

I'm on the editorial board of

• Newsletter of the Korean Mathematical Society

• KIAS Horizon (a webzine for public)

Here's a quote I like: William P. Thurston, in "On proof and progress in mathematics" (1994):

"We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about math."

last updated: Aug. 14, 2026