Perhaps the key theme of my research results published so far can be said to be quantum (higher) Teichmüller theory.

These days, (in Korea) I'm trying to sell myself as belonging to the area of `Geometric Topology', `Quantum Geometry', and `Physical Mathematics' (`Mathematical Physics' in Korea seems to be restricted only to PDE related topics),

with the major theme being `3d Quantum Gravity', or `Quantization of regular functions on higher Teichmüller spaces and cluster varieties'.

To a layman I say either that I study `mysteries of the universe' (and people usually laugh when I say it) or `symmetries' (but I don't say that these days..).

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

• 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

last updated: May 2, 2024