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.
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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.
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)
