# Program

September 26 (Tue)

19:30-21:00 Discussion Session 1September 27 (Wed)

09:30-10:00 Andrés Navas (USACH)

Title:Title: On the (path-)connectedness of spaces of commuting diffeomorphisms.

Abstract: I will elaborate on a recent work with Hélène Eynard-Bontemps, where we show that the space of pairs of commuting diffeomorphisms with absolutely-continuous derivative of a compact 1-manifold is path-connected. The techniques employed also allow to show connectedness in regularity C^2 for the case of the interval. Several questions will be raised along the lectures.

10:00-10:30 Inkang Kim (KIAS)

Title: Dynamics of Convex Projective Structure- Geometry of the Sinai-Ruelle-Bowen Measure

Abstract: We study the Sinai-Ruelle-Bowen Measure, Lyapunov exponants and SRB entropy of convex projective structures. We relate these quantities to the geometry of the boundary at infinity. This is a joint work with Patrick Foulon.

10:30-11:00 Coffee Break

11:00-11:30 Juhun Baik (KAIST)

Title: Monodromy through bifurcation locus of the Mandelbrot set

Abstract: It has been many years to understand how the itinerary sequence changes when the parameter of quadratic complex polynomials varies around the bifurcation points. Classically, the study on dynatomic curves yields a monodromy on the itinerary sequence of given period $n$. In this talk I will introduce an algorithm how each itinerary sequence changes regardless of period for certain bifurcation points. This is a joint work with my advisor Harry Hyungryul Baik (KAIST).

11:30-12:00 Hyungryul Baik (KAIST)

Title: Sol manifolds obtained from a veering pair of laminations

Abstract: TBD

12:00-13:30 Lunch

13:30-14:00 Wenyuan Yang (BICMR, Peking University)

Title: Generic 3-manifolds are hyperbolic

Abstract: In this talk, we first introduce various models to study what a generic 3-manifold looks like. We then focus on the Heegaard splitting model of 3-manifolds, equipped with geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a generic Heegaard splitting goes linearly to the infinity. In particular, generic 3-manifolds are hyperbolic in this model. This represents the joint work with Suzhen Han (AMSS) and Yanqing Zou(ECNU).

14:00-14:30 Sungwoon Kim (Jeju National University)

Title: Structural stability of meandering hyperbolic group actions

Abstract: We introduce a notion of meandering hyperbolic group action generalizing hyperbolic group action on its Gromov boundary. This generalization is substantial enough to encompass actions of certain non-hyperbolic groups, such as actions of uniform lattices in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust and we prove that meandering-hyperbolic actions are still structurally stable.

14:30-15:00 Coffee Break

15:00-15:30 Carl-Fredrik Nyberg Brodda (KIAS)

Title: Decision problems in Baumslag-Solitar-like monoids

Abstract: First, I will present recent results surrounding membership problems in one-relator groups, and how this problem is intricately connected with right-angled Artin groups. Then, using results by Guba (1997) connect membership problems in one-relator groups with the word problem in one-relation monoids, I will describe certain families of one-relation monoids in which the word problem can be solved by appealing to membership problems in solvable Baumslag-Solitar groups. Using recent results by Cadilhac, Chistikov & Zetsche (2021) on the decidability of the rational subset membership problem in solvable Baumslag-Solitar groups, this will yield decidability of the word problem in the constructed one-relation monoids. Thematically, I will attempt to give a crash course in how one-relation monoids can differ from the more familiar one-relator groups.

15:30-16:30 Problem Session 1

18:00-19:30 Dinner

September 28 (Thu)

09:30-10:00 Cristóbal Rivas (Universidad de Chile)

Title: One dimensional representations of Higman's group

Abstract: I will report on a joint work with Michele Triestino regarding representations of Higman's group into the group of homeomorphisms of the real line.

10:00-10:30 KyeongRo Kim (Seoul National University)

Title: An overview of the laminar group theory

Abstract: A laminar group theory is motivated by the Thurston's universal circle theory. In this talk, I will overview the recent developments of the laminar group theory and present the characterization theorems of some Kleinian groups in terms of the number of invariant the circle laminations. This talk is based on the collaborative works with Hyungryul Baik and HongTaek Jung.

10:30-11:00 Coffee Break

11:00-12:00 Problem Session 2

12:00-13:30 Lunch

13:30-15:30 Discussion Session 3