## How to join

Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)

## 2022

June 29 (W). 4 pm Korea (= 3 pm Singapore)

Ser Peow Tan (National University of Singapore)

Identities on the hyperbolic thrice punctured sphere.

Classical identities like the McShane identity, Basmajian identity or Bridgeman identity either are trivial or do not hold on the thrice punctured sphere. A recent result by Basmajian, Parlier and speaker shows that by putting a grading on the cusps of the thrice punctured sphere, one contains infinitely many non-trivial identities. We discuss some interesting aspects of these identities.

June 29 (W), July 4 (M), July 6 (W). 10 am Korea.

Thomas Koberda (University of Virginia)

Mapping class groups, curve graphs, and model theory

In this series of talks, I will give an introduction to the model theory of the curve graph.

Lecture 1. The curve graph and its automorphism. In the first talk, I will discuss some of the combinatorial and geometric properties of the curve graph of an orientable surface of finite type, and how its structure relates to the study of the mapping class group of the surface. I will concentrate on automorphisms of curve graphs, and discuss the context surrounding Ivanov's metaconjecture concerning "natural" graphs associated to surfaces and their automorphisms.

Lecture 2. An introduction to model theory. I will survey some of the basic notions of model theory, with examples. The main points will be the notion of interpretability, quantifier elimination, stability, and Morley rank. Finally, I will formulate Ivanov's metaconjecture as a precise model-theoretic statement.

Lecture 3. The model theory of the curve graph. I will survey joint work with V. Disarlo and J. de la Nuez Gonzalez about the model theory of the curve graph. Topics will include quantifier elimination, $\omega$-stability, non-definability of certain natural subsets of the curve graph, lack of mutual interpretability between certain geometric graphs, and interpretation rigidity between curve graphs.

March 10 (Th) 9 -10am Korea

Tao Li (Boston College)

Taut foliations of 3-manifolds with Heegaard genus two

Let M be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of M is left-orderable then M admits a co-orientable taut foliation.

Mar 3 (Th) 10 -11 am Korea

Mar 4 (F) 9:30 - 10:30 am Korea

Lei Chen (University of Maryland, College Park)

Talk 1: Nielsen realization problem.

For the natural projection Diff(S_g) ->MCG(S_g), when does this map have a section? MCG(S_g) := \pi_0(Diff(S_g)).

Talk 2: Homomorphism between MCG(S_g) and MCG(S_h), and between different braid groups.

Even more, how can MCG(S_g) acts on spheres?

### Organizers

Harry Hyungryul Baik (KAIST)

Sam Sang-hyun Kim (KIAS)