Conference & Workshop

PMI-SNU Quantum Topology Winter School

Date: 2016 Feb 15 - 19
Place: SNU (Sangsan 406)
첨부파일: poster.jpg
PMI-SNU Quantum Topology Winter School

*Date: 2016/02/15~2016/02/19
*Place: #406, 129 Sangsan Math.Sci.Bldg, Seoul National University

Jinseok Cho (PMI, POSTECH)
Hyuk Kim (Seoul National University)

Jinseok Cho (PMI, POSTECH)
Hee Joong Chung (KIAS)
Hyun Kyu Kim (KIAS)

*Title & Abstract
1) Hyun Kyu Kim (KIAS)
Title : Teichmüller space, cluster algebra, and their quantization
Abstract : My series of lectures is divided roughly into three parts. First is introduction of basic aspects of the theory of cluster algebras, which was initiated by Fomin and Zelevinsky at around early 2000's. I will start by easy definitions and examples using quivers, and will refine the definition as we move on. Second is about cluster varieties, in the sense of Fock and Goncharov. One can think of cluster varieties as algebro-geometric spaces whose rings of functions are cluster algebras. As a special case, we will realize classical Teichmuller spaces as examples of cluster varieties. Third is about quantization.
The commutative rings will be replaced by non-commutative rings of operators on Hilbert spaces, along with the corresponding mutation maps. No prior knowledge on the subject is assumed. I will use only very basic notions in elementary algebra, algebraic geometry, and analysis.

2) Hee Joong Chung (KIAS)
Title : Topics in Chern-Simons Theory
Abstract : We will firstly introduce some physics background for later discussion. Then we will move on to Chern-Simons theory with compact and complex gauge group. Also, some recent developments including state integral model will be discussed.

3) Jinseok Cho (PMI, POSTECH)
Title : Cluster algebra on the braids
Abstract : We will introduce the cluster algebra of the braids proposed by Hikami-Inoue and its relation to the hyperbolic structures of links.
Then the answer to the Hikami-Inoue conjecture will be given.

*Contact: Jinseok Cho (