Schedule/Abstracts

Abstracts/Lecture Notes

Speaker: Gye-Seon Lee

Abstract: 

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This lecture particularly focuses on how one can use Coxeter groups to construct interesting examples of discrete subgroups of Lie groups.

Speaker: Hongtaek Jung

Abstracts: 

(1) Survey talk: Introduction to Hitchin components

Hitchin components are direct descendants of the Teichmuller space and one of the well-known examples of higher Teichmuller spaces. We first discuss various characterizations of Hitchin components and explore their basic properties. In the second part of the talk, we focus on Labourie's work on Hitchin components and Anosov representations.

(2) Research talk: Volumes of Hitchin-Riemann moduli spaces are infinite

Let Hit_n(S) be the PSL(n,R)-Hitchin component of a compact surface S with negative Euler characteristic and let Mod(S) be the mapping class group. We discuss the Atiyah-Bott-Goldman volumes of the Hitchin-Riemann moduli spaces Hit_n(S)/Mod(S). When n=2, M. Mirzakhani proved that the Atiyah-Bott-Goldman volume, or equivalently the Weil-Petersson volume, of Hit_2(S)/Mod(S) is finite. On the contrary, we show that the volumes of Hit_n(S)/Mod(S) are infinite provided n>2.  This is joint work with Suhyoung Choi.

Speaker: Sungwoon Kim

Title: Kleinian groups 

Abstract: 

A Kleinian group is a discrete group of the isometry group of hyperbolic space. It has been a central theme in hyperbolic geometry. In this lecture, I will review basic notions and important results in Kleinian group theory. In particular, Bers theorem, Ahlfors finiteness theorem and Maskit combination theorem are intensively covered.

Speaker: Suhyoung Choi

Abstract: 

In part 1 of the survey talks, we will cover the aspects of the discrete group theory, including the Poincare fundamental polyhedron theorem and the topology of orbifolds including covering orbifolds. 

In part 2 of the survey talks, we will cover the theory of 2-orbifolds by Thurston and the theory of geometric structures on orbifolds including the deformation spaces and Ehresmann-Thurston principles. 

The survey will be based on "Geometric structures on 2-orbifolds: exploration of discrete symmetry

MSJ Memoirs, Vol. 27. 171pp + xii,  2012. World Scientific Pub. Co." (See my homepage.)

Lecture Slides:

Discussion session on Research problems and direction

Schedules

8/16 Wednesday

-14:00~14:50 Suhyoung Choi

Survey talk, Part 1: Discrete group theory, topology of orbifolds

-15:00~15:50 Suhyoung Choi

Survey talk, Part 2: Theory of 2-orbifolds, geometric structures on orbifolds

-16:00~16:50 Hongtaek Jung

Survey talk: Introduction to Hitchin components

-17:00~19:00 Dinner

8/17 Thursday

-10:00~10:50 Hongtaek Jung

Survey talk: Introduction to Hitchin components

-11:00~11:50 Hongtaek Jung

Research Talk: Volumes of Hitchin-Riemann moduli spaces are infinite

Afternoon

-14:00~14:50 Sungwoon Kim (via Zoom)

Kleinian groups

-15:00~15:50 Sungwoon Kim (via Zoom)

Kleinian groups

-16:00~16:50 Suhyoung Choi, Gye-Seon Lee, Sungwoon Kim

Discussion session on Research methodology

-17:00~19:00 Dinner

8/18 Friday

-9:00~9:50 Gye-Seon Lee

Coxeter groups

-10:00~10:50 Gye-Seon Lee

Coxeter groups

-11:00~11:50 Suhyoung Choi, Gye-Seon Lee, Sungwoon Kim, Hongtaek Jung

Discussion session on Research problems and direction

-12:00~14:00 Lunch

※ Dinners for Wednesday, Thursday and lunch for Friday will be provided.