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 We are pleased to host a Korea-France Workshop on Dynamical Group Theory. At this event, we will promote interaction among the researchers from this pair of countries, along with other international participants. Talks and discussions of this event will focus on dynamical, algebraic and topological properties of group actions.

Date

February 29, 2024 (Thursday)

Venue

 June E Huh Center for Mathematical Challenges (HCMC) of KIAS, 2nd floor of Soo-rim Art Center [Google Map]

Speakers

Michele Triestino (Dijon)

Nicolas Matte Bon (Lyon)

Inhyeok Choi (KIAS)

Carl-Fredrik Nyberg-Brodda (KIAS)

Local Organizers 

Sang-hyun Kim (KIAS)

Carl-Fredrik Nyberg-Brodda (KIAS)

Contact

Carl-Fredrik Nyberg-Brodda: cfnb@kias.re.kr 

Sponsors

National Research Foundation of Korea (RS-2023-00278510)

Korea Institute for Advanced Study (KIAS)

Michele Triestino:

Title: Moduli spaces of group actions on the line

Abstract: Given a finitely generated group G, the possible actions of G on the real line (without global fixed points), considered up to semi-conjugacy, are encoded by the space of orbits of a flow on a compact space naturally associated to G, that we call the Deroin space of G. In joint works with J. Brum, C. Rivas and M. Triestino, we study the Deroin space for several classes of groups (including solvable groups and groups like Thompson's F), and use it to deduce rigidity and flexibility results of actions under small perturbations.

Nicolás Matte-bon:

Title:  Some structure theorems for group actions on the line by C^1-diffeomorphisms

Abstract: It is well-known that a countable group embeds in the group of (orientation preserving) homeomorphisms if and only if it is left-orderable. In this talk I will explain a classification theorem for all C^1-actions on the line of a class of left-orderable groups, called locally moving groups, a famous example of which is Thompson’s group F. In particular all faithful minimal actions of such a group by C^1-diffeomorphisms are topologically conjugate to a “standard” model. The proof relies on a description of the dynamics possible actions on the line of such groups by C^0 homeomorphisms, which turn out to be much more abundant. If time permits, I shall explain how similar ideas allow to show that all C^1 actions of a finitely generated solvable group on a real interval are semi-conjugate to an action by affine transformations of the real line. Based on a series of works with J. Brum, C. Rivas and M. Triestino.

Inhyeok Choi:

Title: Normal subgroups, confined subgroups and growth

Abstract: In a hyperbolic group G, every infinite normal subgroup N is at least half-larger than the ambient group G: the growth rate of N is greater than half of the growth rate of G. Moreover, this lower bound is sharp. Recently there have been efforts to generalize this to (1) different types of group actions and (2) different types of subgroups. I will describe an analogous problem for confined subgroups and explain Gekhtman-Levit’s recent result. This is related to an ongoing project with Ilya Gekhtman, Wenyuan Yang and Tianyi Zheng.

Carl-Fredrik Nyberg-Brodda:

Title: The freeness problem for parabolic subgroups of SL(2,Q)

Abstract: I will discuss some recent progress on the freeness problem for groups of 2x2 rational matrices generated by two parabolic matrices. In particular, I will discuss recent progress on determining the structural properties of such groups (beyond freeness) and when they have finite index in the finitely presented group SL(2,Z[1/m]), for appropriately chosen m.