## 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.

## 2023 Fall

All talks are in-person & online, unless noted otherwise.

Aug 9 (W at 2 pm), Sungkyung Kang (IBS-CGP)

Aug 31 (TH at 10 & 11:15 am), Thomas Scanlon (Berkeley)

Sep 5, 7 (Tu/Th at 10 - 11:30 am), Alan Reid (Rice)

Sep 19, 20 (Tu/W at 10 am), Andrés Navas (USACH)

Sep 26 (Tu at 10 am), Cristóbal Rivas (U Chile)

Oct 12 (Th at 11am, online only), Nicholas Vlamis (CUNY Queens)

Oct 24 (Tu at 11 am), Thomas Koberda (U Virginia)

Oct 28 (Sa, morning, in-person only), GGT Session, KMS Fall Meeting, Seoul National University

Oct 31 (Tu at 11 am), Seokbum Yoon (SUSTech)

Nov 2 (Th at 11 am), Robert Tang (Xi'an Jiaotong-Liverpool)

Nov 7, 9 (Tu, TH at 11 am), Shuhei Maruyama (Kanazawa University)

Nov 16 (Th at 11 am), Minkyu Kim (KIAS)

Nov 17 (F at 11 am), Geunho Lim (Einstein Institute of Mathematics, Hebrew University of Jerusalem)

Nov 20 (M at 11 am), Don-Sung Lee (SNU)

Nov 20 (M at 3 pm), Heejoung Kim (KPU)

Nov 23 (Th at 11 am), James Rickards (Colorado)

Dec 5 (Tu at 11 am), Javier de le Nuez-Gonzalez (KIAS)

Dec 7 (Th at 2 pm), Tara Brendle (University of Glasgow)

November 20, 2023 (Tu) at 11 am

In person KIAS (1424)

Online http://kimsh.kr/vz

Refreshment KIAS lounge, 10:30 am

Don-Sung Lee (SNU)

Salter's question on the image of the Burau representation of B_3

In 1974, Birman posed the question of under what conditions a matrix with Laurent polynomial entries is in the image of the Burau representation. In 1984, Squier observed that the matrices in the image are contained in a unitary group. In 2020, Salter formulated a specific question: whether the central quotient of the Burau image group is the central quotient of a certain subgroup of the unitary group. We solve this question negatively in the simplest nontrivial case, n=3, algorithmically constructing a counterexample. In addition, we investigate analogous questions by changing the base ring from \mathbb{Z} to \mathbb{F}_{p} by taking modulo p. This is still meaningful, as the Burau representation modulo p is faithful when n=3 for every prime p. We answer the questions affirmatively when p=2, and negatively when p>2.November 20, 2023 (M) at 3 pm

In person KAIST (E6-1, 4407)

Online http://kimsh.kr/vz

Heejoung Kim (KPU)

Mapping class groups of infinite-type surfaces and surface Houghton groups

The mapping class group Map(S) of a surface S is the group of isotopy classes of diffeomorphisms of S. When S is a finite-type surface, the classical mapping class group Map(S) has been well understood. On the other hand, there are recent developments on mapping class groups of infinite-type surfaces. In this talk, we discuss mapping class groups of finite-type and infinite-type surfaces and elements of these groups. Also, we define surface Houghton groups, which are subgroups of mapping class groups of certain infinite-type surfaces. Then we discuss finiteness properties of surface Houghton groups, which is a joint work with Aramayona, Bux, and Leininger.

November 23, 2023 (Thursday) at 11 am

In person KIAS (1424)

Online http://kimsh.kr/vz

James Rickards (Colorado)

Failure of the local-global conjecture in thin (semi)groups

The study of orbits of thin (semi)groups encapsulates many famous problems, including Zaremba's conjecture and Apollonian circle packings. The local-global conjecture states that as long as the (semi)group is big enough, every large enough integer that satisfies certain congruence restrictions will appear in an orbit. In a recent breakthrough, this conjecture was proven to be false for many Apollonian circle packings. We will discuss the history of the conjecture, this recent work, and give new examples of thin semigroups where the conjecture is false.

December 5, 2023 (Tuesday) at 11 am

In person KIAS (1423)

Online http://kimsh.kr/vz

Javier de la Nuez-González (KIAS)

Minimality of the compact-open topology on diffeomorphism and homeomorphism groups

We will talk about recent work in which we prove that the restriction of the compact-open topology to the diffeomorphism group of a manifold without boundary of dimension different from 3 is a minimal element of the lattice of Hausdorff group topologies on the group. If the dimension is also different from 4 it follows that the same holds for the compact-open topology on the homeomophism group, which combined with K. Mann's automatic continuity results implies the latter admits a unique separable Hausdorff group topology

December 7, 2023 (Thursday) at 2 pm

In person KIAS (1423)

Online http://kimsh.kr/vz

Tara Brendle (University of Glasgow)

Semi-direct product structures in mapping class groups of 3-manifolds

We will show that a certain short exact sequence associated with mapping class groups of 3-manifolds admits a splitting. One by-product of this result is that Out(F_n) arises as a certain stabilizer subgroup of the mapping class group of a connected sum of n copies of S2 x S1. The general case is slightly more complicated: using recent work of Chen-Tshishiku, we will describe the second factor in the semi-direct product structure in terms of the prime decomposition of the 3-manifold. This is joint work with Nathan Broaddus and Andrew Putman.

## 2024

March 27, 29, 2023 (Tue/Thur) 2023 at 11 am (tentative)

Michele Triestino (Université de Bourgogne)

TBA

TBA