Virtual Seminar on 

Geometry and Topology

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

Organizer

Hyungryul Baik (KAIST), Sang-hyun Kim (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

May 13, 2024 (Mon), 3 - 4 pm

KIAS 1503

Sam Nariman (Purdue)

Groupoids, diffeomorphisms, and invariants of foliations

In this talk, we will discuss the equivariant version of Mather-Thurston’s theorem that relates the group cohomology of diffeomorphism groups to the classifying space of the groupoid of germs. I will explain two applications of this perspective. One is about PL homeomorphisms of surfaces. We discuss that Greenberg's work on PL foliations can be used to answer the case of surfaces of a question posed by Epstein in 1970 about the simplicity of PL homeomorphisms that are isotopic to the identity., I will talk about another application for invariants of flat sphere bundles which answers a question posed by Haefliger. For example, we will see that for G a finite-dimensional connected Lie group, any principal G-bundle over a closed manifold is cobordant via $G$-bundles to a foliated G-bundle (not necessarily flat principal G-bundle).

May 14, 2024 (Tu), 11 -12 pm

KIAS 1423

Sam Nariman (Purdue)

The bounded cohomology of transformation groups of Euclidean spaces and discs

In this talk, I will first talk about a joint work with N. Monod about a method to calculate the bounded cohomology of the diffeomorphism group of spheres. Then I will report on a work in progress with Francesco Fournier-Facio and Nicolas Monod on the bounded cohomology of Homeo(R^n) and Homeo(D^n).


May 16, 2024 (Th)


KIAS 1503


2 pm - 3 pm: Katada Mai (Kyushu University)

The category of Jacobi diagrams in handlebodies

The Kontsevich invariant, which is a strong quantum invariant, for links or (bottom) tangles takes values in the spaces of Jacobi diagrams. Habiro and Massuyeau introduced the category of Jacobi diagrams in handlebodies and extended the Kontsevich invariant to a functor. In the second talk , we will use the composition of morphisms in this category to define a polynomial functor.


3 pm - 4 pm: Minkyu Kim (KIAS)


Polynomial functors on free groups.

Polynomial functors naturally arise in various areas such as representation theory and algebraic topology. In this talk, we mainly describe algebraic aspects of polynomial (analytic) functors on the opposite category of free groups. In particular, we explain Powell’s adjunction between the category of polynomial (analytic) functors and the representation category of the Lie operad. If time is allowed, we mention some results under the assumption that such functors are symmetric monoidal.



May 17, 2024.


KIAS 7323


2 pm - 3 pm: Katada Mai (Kyushu University)

The polynomial functor associated with the spaces of Jacobi diagrams

By using the composition of morphisms in the category of Jacobi diagrams in handlebodies, we define a polynomial functor from the opposite category of the category of finitely generated free groups. We will observe some properties of this functor.


3 pm - 4 pm: Minkyu Kim (KIAS)

Polynomial ideal and primitivity ideal.

The goal of this talk is to reveal a principle behind some well-known adjunctions: the adjunction which yields Morita equivalence between the ground ring and the matrix algebra; and Powell’s adjunction of the first talk. This is described by using a generalization of eigen-ring construction in classical algebra theory. In application, Powell’s adjunction is refined by introducing two ideals of the linearization of the opposite category of free groups: polynomial ideal and primitivity ideal. We would like to explain relation between these ideals and the Lie operad.

May 30, 2024, KIAS 1423

Donggyun Seo (Seoul National University)

Pants decomposition of free groups

A pants decomposition of a surface is a fundamental tool in Teichmüller theory. We define a pants decomposition of a free group as the pants decomposition of a compact orientable surface whose fundamental group is the free group. In this talk, I will introduce my ongoing project on the pants decomposition of free groups and explain some properties of the pants graphs of free groups.

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. 

Mini-course Emmanuel Militon

Invited talks Collin Bleak, Lei Chen, Thomas Koberda, Andre Nies (Auckland), Javier de la Nuez-Gonzalez, Yash Lodha (to be confirmed)

Organizers


September 25 - 28, 2024 

Workshop Dynamical Group Theory IV

Webpage in construction.

Invited talks Chris Leininger (Rice), Alan Reid (Rice), Koji Fujiwara (Kyoto)

Organizers

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)

Organizers

Harry Hyungryul Baik (KAIST)

Sam Sang-hyun Kim (KIAS)

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