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(1) May 16, 2024.
KIAS 1423
2 pm - 3 pm: Katada Mai (Kyushu University)
The category of Jacobi diagrams in handlebodies Abstract：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. Abstract: 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.
(2) May 17, 2024.
KIAS 1423
2 pm - 3 pm: Katada Mai (Kyushu University)
The polynomial functor associated with the spaces of Jacobi diagrams Abstract: 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. Abstract: 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.