September 26 (Tue)
19:30-21:00 Discussion Session 1
September 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.
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
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
13:30-15:30 Discussion Session 3