## Organizer

Hyungryul Baik (KAIST), Sang-hyun Kim (KIAS)

## How to join

Zoom http://kimsh.kr/vz

Meeting ID: 822 3235 0014

Passcode: 7998

Time Generally, Tuesday or Thursday 11 am KST

Length is typically for one-hour unless noted otherwise, although it's often extended by questions etc.

## 2024

Jan 23 and 25, 2024 (Tu and Th) at 11 am - noon

KIAS 1503

Ken'ichi Ohshika (Gakushuin)

Thurston’s broken windows only theorem and his proof of the bounded image theorem (Parts 1, 2)

Both the broken windows only theorem and the bounded image theorem constitute important parts of Thurston’s proof of the unifomisation theorem for Haken manifolds dated back to the early 1980s. According to his plan of proofs, the proof for the bounded image theorem relies essentially on the broken windows only theorem, in particular its second statement. We show that this second statement has counter examples. Although we can fix it by weakening the result, this weak form cannot be used for the proof of the bounded image theorem. We will also explain how the bounded image theorem (whose proof was recently given by Cyril Lecuire and myself) would follow, if this second statement were true.

Feb 26 (Mon 3-4 pm), Feb 27 (Tue 2-3 pm)

KIAS 1423

Michele Triestino (Université de Bourgogne)

Nicolás Matte Bon (Institut Camille Jordan - Université Lyon 1)

Laminations and structure theorems for group actions on the line (Part 1,2)

A lamination of the real line is a closed collection of pairwise unliked, finite intervals. They appear naturally when studying certain classes of group actions on the line. More precisely, we will discuss actions of solvable groups, and of locally moving groups (these are subgroups of Homeo(R) such that for any open interval I, the subgroups of elements fixing the complement of I acts minimally on I). A famous exampke of a locally moving group is Thompson's group F. Both classes admit "standard models" of actions on the line: solvable groups act by affine transformations, whereas locally moving groups have their defining actions. We prove a structure theorem which says that any minimal faithful action of a finitely generated group in this class is either standard, or preserves a lamination. Moreover, the large scale dynamics of actions preserving laminations can be described in terms of the standard actions. We will briefly mention the results for solvable groups, and focus the discussion on locally moving groups. This is based on works with J. Brum and C. Rivas.

Feb 29 (Thur 10 am - 5 pm), 2024

Korea-France Workshop on Dynamical Group Theory (KIAS)

https://kimsh.kr/dgt-kf

Mar 26, 2024 (Tue) 11 am (tentative)

Minh Nhat Doan (VAST / NUS)

TBA

TBA

May 14, 2024 (Tue) 11 am (tentative)

Sam Nariman (Purdue)

June 18, 2024 (Tue) 11 am (tentative)

Alan Reid (Rice)

July 9, 2024 (Tue) 11 am (tentative)

Thomas Koberda (Virginia)

July 23, 2024 (Tue) 11 am (tentative)

Chris Leininger (Rice)

August 27, 2024 (Tue) 11 am (tentative)

Ser Peow Tan (NUS)