KIAS Topology Seminar


About

The KIAS Topology seminar is one of the regular group seminars at Korea Institute for Advanced Study (KIAS). The goal is to invite researchers working on topology to give seminar talks and share their expertise. The topics include low-dimensional topology, symplectic and contact topology, algebraic topology, toric topology, Homotopy Algebra, DG Geometry, Poisson Geometry, algebraic K-theory, topological quantum field theory, category theory and any other related subjects. For more information about the seminar, contact the webmaster.

The Organizers: Youngjin Bae, Dongwook Choa, Hakho Choi, Joontae Kim, Sangwook Lee, Hsuan-Yi Liao, and Jongbaek Song.

Schedule, Year 2020

  • 29 December 2020 14:00--16:00, Online (Zoom meeting ID: 858 1496 2706, No passcode! Click here to enter)
    Lagrangian fillings of ADE-type Legendrians
    Youngjin Bae (Incheon National University, Incheon)
    I will introduce Legendrian links of ADE-type Dynkin diagrams. Then I argue that there are at least as many Lagrangian fillings as seeds in the corresponding cluster structure. The main ingredients are N-graphs developed by Casals-Zaslow, and finite type cluster structures by Fomin-Zelevinsky. This is a joint work in progress with ByungHee An and Eunjeong Lee.
    (Click here for the Slide!)

  • 28 December 2020 14:00--16:00, Online (Zoom meeting ID: 838 3852 4614, No passcode! Click here to enter)
    Generalized Kodaira-Spencer maps
    Sangwook Lee (Soongsil University, Seoul)
    We study the mirror symmetry between cohomology algebras on A- and B-models. On A-model, we are given a quantum cohomology or a symplectic cohomology, and on B-model we are given a Jacobian algebra or a Koszul algebra. First we recall the Kodaira-Spencer map due to Fukaya-Oh-Ohta-Ono. Then we deal with a case when the target is not a genuine Jacobian algebra, especially when there is a finite group action hence the target is an orbifold Jacobian algebra. In this case we are led to consider more general closed-open maps which we named generalized Kodaira-Spencer maps. We also consider noncompact cases so that we need to think of symplectic cohomology and Koszul algebra respectively. This is based on the joint work with C.-H. Cho.

  • 18 December 2020 14:00--16:00, Online (Zoom meeting ID: 850 0778 0890, No Passcode!)
    Homological mirror symmetry for invertible curve singularities
    Wonbo Jeong (Seoul National University, Seoul)
    For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on the wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in singularity theory. As an application, we formulate a full version of Berglund-Hübsch homological mirror symmetry. We prove it for the case of two variables by constructing a functor from our new Fukaya category to the matrix factorization category. This is a joint work with Cheol-hyun Cho (SNU) and Dongwook Choa (KIAS).

  • 12 November 2020 16:00--17:00, Online (Zoom meeting ID: 856 3201 5914 Passcode: 368169)
    Graph complexes and quantization of Lie bialgebroids and Courant algebroids
    Kevin Morand (Sogang University, Seoul)
    In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a graph version of the deformation theory for Poisson structures. In this talk, we will review Kontsevich’s graph construction and the role it plays in deformation quantization before providing a generalisation suitable to understand the deformation theory of Lie algebroids and Courant algebroids as well as their respective quantizations.

  • 16 June 2020 16:30--17:30, Online (Contact Joontae Kim for an invitation)
    Symmetries and global surfaces of section on the tight three-sphere
    Seongchan Kim (Université de Neuchâtel, Swiss)
    In this talk, I will report the existence result of a disc-like global surface of section on the tight three-sphere, which is invariant under given symmetries. As an application, the Hénon-Heiles system will be discussed.

  • 15 June 2020 17:00--18:30, Online (Contact Youngjin Bae for an invitation)
    Fiber Floer cohomology and conormal stops
    Johan Asplund (Uppsala University, Sweden)
    Let S be a closed, orientable, spin manifold, let K ⊂ S be a submanifold and let F be a cotangent fiber in T*S. In this talk we show that the partially wrapped Floer cochains of F stopped by the unit conormal of K is A_∞-isomorphic to chains of a Morse theoretic model of the based loop space of S \ K. The isomorphism is constructed by counting holomorphic curves. If time permits, we will discuss how this isomorphism can be used to relate the partially wrapped Floer cohomology of F to the Alexander invariant of K in case K ⊂ S^n belongs to a certain family of codimension 2 knots.
    (Click here for the Slide!)

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    Address: 85 Hoegiro Dongdaemungu, Seoul 02455, Republic of Korea

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