41 citations · 111 across the 22 of their papers we have counts for
22 papers
A trilogy of mapping class group representations from three-dimensional quantum gravity
Hyun Kyu Kim
For a punctured surface , the author and Scarinci (arXiv:2112.13329) have recently constructed a quantization of a moduli space of Lorentzian metrics on the 3-manifol…
Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
Hyun Kyu Kim
A new canonical Hopf algebra called the quantum pseudo-Kähler plane is introduced. This quantum group can be viewed as a deformation quantization of the complex two-dimensional pla…
A quantization of moduli spaces of 3-dimensional gravity
Hyun Kyu Kim, Carlos Scarinci
We construct a quantization of the moduli space of maximal globally hyperbolic Lorentzian metrics on with constant sectiona…
Three dimensional construction of the Virasoro-Bott group
Igor B. Frenkel, Hyun Kyu Kim
We present a three-dimensional geometric construction of the Virasoro-Bott group, which is a central extension of the group of diffeomorphisms of the circle. Our approach is analog…
Naturality of quantum trace maps for surfaces
Hyun Kyu Kim
Fock-Goncharov's moduli spaces of framed -local systems on punctured surfaces provide prominent examples of cluster $\m…
-laminations as bases for cluster varieties for surfaces
Hyun Kyu Kim
In this paper we partially settle Fock-Goncharov's duality conjecture for cluster varieties associated to their moduli spaces of -local systems on a punctured surface $\fr…