Virtual Seminar on 

Geometry and Topology

https://sites.google.com/view/visgat

Organizers

Hyungryul Baik (KAIST),
Sang-hyun Kim, Sanghoon Kwak, Javier de la Nuez-González, Carl-Fredrik Nyberg-Brodda (KIAS)

How to join

Zoom https://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.

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2024

November 26th, 2024 (Tue), 11 am

Zoom only https://kimsh.kr/vz

Katherine Williams Booth (Vanderbilt)

Automorphisms of the smooth fine curve graph 

The smooth fine curve graph of a surface is an analogue of the fine curve graph that only contains smooth curves. It is natural to guess that the automorphism group of the smooth fine curve graph is isomorphic to the diffeomorphism group of the surface. But it has recently been shown that this is not the case. In this talk, I will give several more examples with increasingly wild behavior and give a characterization of this automorphism group for the particular case of continuously differentiable curves.  


Two joint seminars with KIAS HCMC Topology Seminar

Zoom only (link) | Meeting ID: 819 2513 6908 | Passcode: kias

Mladen Bestvina (University of Utah)

Classification of Stable Surfaces with respect to Automatic Continuity

We provide a complete classification of when the homeomorphism group of a stable surface, Σ, has the automatic continuity property: Any homomorphism from Homeo(Σ) to a separable group is necessarily continuous. This result descends to a classification of when the mapping class group of Σ has the automatic continuity property. Towards this classification, we provide a general framework for proving automatic continuity for groups of homeomorphisms. Applying this framework, we also show that the homeomorphism group of any stable second countable Stone space has the automatic continuity property. Under the presence of stability this answers two questions of Mann. This is joint work with George Domat and Kasra Rafi.


Zoom only (link) | Meeting ID: 819 2513 6908 | Passcode: kias

George Domat (University of Michigan)

Graphical models for topological groups

By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley-Abels graph of a totally disconnected, locally compact group, we introduce countable connected graphs associated to Polish groups that we term Cayley-Abels-Rosendal graphs. A group admitting a Cayley-Abels-Rosendal graph acts on it continuously, coarsely metrically properly and cocompactly by isometries of the path metric. By an expansion of the Milnor-Schwarz lemma, it follows that the group is generated by a coarsely bounded set and is quasi-isometric to the graph. In other words, groups admitting Cayley-Abels-Rosendal graphs are topological analogues of the finitely generated groups. We will see these concepts in action by considering homeomorphism groups of countable Stone spaces (i.e. homeomorphism groups of countable end spaces/countable ordinals). We completely characterize when these homeomorphism groups are coarsely bounded, when they are locally bounded (all of them are), and when they admit a Cayley-Abels-Rosendal graph, and if so produce a coarsely bounded generating set. This is joint work with Beth Branman, Hannah Hoganson, and Robbie Lyman.


January 16th (Thu) 2025, 11 am 

KIAS 1424 & Zoom https://kimsh.kr/vz

Inhyeok Choi (KIAS / Cornell)

Free discrete subgroups of Homeo(S) and the fine curve graph.

Recently, Bowden-Hensel-Webb proposed the notion of the fine curve graph for the study of Homeo(S) as an analogue of the curve graph for the mapping class group Mod(S). In the case of Mod(S), the orbit map from a subgroup of Mod(S) to the curve graph may be seriously distorted. In this talk, I will describe an analogous example for Homeo(S) acting on the fine curve graph, namely, a free discrete subgroup of Homeo(S) without global fixed points, whose one free factor is a loxodromic and the other one free factor fixes the basepoint on the fine curve graph. If time allows, I will explain why the (metric) WPD of point-pushing pseudo-Anosov maps help understand this subgroup. This project is in progress. 

Organizers

Hyungryul Baik (KAIST)

Sang-hyun Kim, Sanghoon Kwak, Javier de la Nuez-González, Carl-Fredrik Nyberg-Brodda (KIAS)


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