## 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, Tuesdays or Thursdays 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)

March 14 (Thu 2 pm - 3pm), 2024

KIAS 1423

Paolo Marimon (Vienna)

Minimal operations over permutation groups

Joint work with Michael Pinsker. Let B be a fixed relational structure (e.g. a graph). The Constraint Satisfaction Problem for B, CSP(B), is the computational problem of, given a finite structure A in the same language, deciding whether there is a homomorphism from A into B. Many natural problems in computational complexity can be framed in this fashion. When the structure B is finite, we know that CSP(B) is always in NP, and, assuming P \neq NP, we know that whether this problem is in P or NP-complete can be characterised in terms of identities satisfied by the polymorphisms of B (a higher arity generalisation of homomorphisms) (Bulatov 2017, Zhuk 2017).

We are interested in generalising the tools used to study constraint satisfaction problems for finite structures to some infinite structures with many symmetries (finitely bounded homogeneous structures). Since understanding the polymorphisms of B is essential to understand the computational complexity of CSP(B), it is often helpful to find polymorphisms of low arity behaving in some non-trivial way. For this reason, we study what are called the minimal polymorphisms above the automorphism group of B. We carry out a classification of the types of minimal operations which may appear over an arbitrary permutation group G\acts B, generalising the work of Rosenberg (1986) for the trivial group and of Bodirsky and Chen (2007) for oligomorphic permutation groups. This allows us to answer some open problems mentioned by Bodirsky (2021) in his book on infinite domain CSPs.

March 28, 2024. 10:30 am - 12 pm (Note the time!)

KIAS 1423

Nhat Minh Doan (VAST / NUS)

Optimal special polygon for congruence subgroup $\Gamma_0(p^n)$.

For a positive integer $n>1$ and a prime $p$, we show that $\Gamma_0(p^n)$ possesses a special fundamental domain (in the sense of Kulkarni) with its cusp set encoded using a Farey sequence of denominators less than or equal to $(f_{p+1}/2)p^{n-1}+f_pp^{n/2}$, where $f_m$ is the m-th Fibonacci number ($f_1=f_2=1, f_m=f_{m-1}+f_{m-2}$ for all $m\in \mathbb{N}$). In the special case where $p=2$, we establish a sharp upper bound of $2^{n-1}$. This is join work with Sang-hyun Kim, Mong Lung Lang, and Ser Peow Tan.

May 9, 2024. 11 am - 12 pm

KIAS 1423

Carl-Fredrik Nyberg-Brodda (KIAS)

TBA

TBA

July 1 - 5, 2024, KIAS (HCMC)

Conference Semigroups, Groupoids, C*-algebras

August 13 - 16, 2024

Workshop Dynamical Group Theory III - New methods in Group Actions on Manifolds

Webpage in construction.

September 25 - 28, 2024

Workshop Dynamical Group Theory IV

Webpage in construction.

Confirmed speakers: Chris Leininger (Rice), Alan Reid (Rice), Koji Fujiwara (Kyoto)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)