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, algebraic geometry, and any other related subjects. For more information about the seminar, contact the webmaster.

The Organizers: Dongwook Choa, Hakho Choi, Joontae Kim, Seongchan Kim, and Jongbaek Song.

Schedule, Year 2021

  • 15 December 2021 16:00--18:00, Online (Contact Seongchan Kim for zoom information)
    An invitation to b-contact topology and Reeb dynamics
    Cédric Oms (the Unit of Pure and Applied Mathematics (UMPA, Lyon), France)
    In this talk we will state a generalization of the Weinstein conjecture in the case of contact structures that admit codimension 1 singularities called b-contact forms. We will prove a weak version of this conjecture for ’generic’ contact forms: more precisely, we show that its associated Reeb vector fields admit escape orbits. This is done by connecting the dynamics of those vector fields to Beltrami vector fields (coming from hydrodynamics) and making use of genericity results for eigenfunctions of the Laplacian à la Uhlenbeck. This is joint work with Eva Miranda and Daniel Peralta–Salas.

  • 8 December 2021 16:00--18:00, Online (Contact Seongchan Kim for zoom information)
    Big Fiber Theorems and Ideal-Valued Measures in Symplectic Topology
    Yaniv Ganor (Technion - Israel Institute of Technology, Israel)
    In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case. We will discuss three examples of such theorems, coming from combinatorics, topology and symplectic topology from a unified viewpoint provided by Gromov's notion of ideal-valued measures. We adapt the latter notion to the realm of symplectic topology, using an enhancement of Varolgunes’ relative symplectic cohomology to include cohomology of pairs. This allows us to prove symplectic analogues for the first two theorems, yielding new symplectic rigidity results. Necessary preliminaries will be explained. The talk is based on a joint work with Adi Dickstein, Leonid Polterovich and Frol Zapolsky.

  • 30 November 2021 16:00--18:00, Online (Zoom link, Zoom Meeting ID: 811 2950 9916, Passcode: 090518)
    On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity
    Jongmyeong Kim (IBS-CGP, Pohang)
    In topological dynamics, the Gromov-Yomdin theorem states that the topological entropy of a holomorphic automorphism $f$ of a smooth projective variety is equal to the logarithm of the spectral radius of the pullback $f^*$ induced on cohomology. In order to establish a categorical analogue of the Gromov-Yomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this talk, we propose a notion that categorifies and generalizes that of a holomorphic automorphism and prove that the Gromov-Yomdin type theorem holds for them. This talk is based on a joint work with Federico Barbacovi.

  • 22 November 2021 15:00--17:00, Online (Zoom link)
    Lefschetz fibrations on plumbings of cotangent bundle of a sphere along trees
    Sangjin Lee (IBS-CGP, Pohang)
    In this talk, I will give an algorithm producing Lefschetz fibrations defined on any plumbing space of $T^*S^n$s where the plumbing pattern is a tree. As a corollary, we can generate diffeomorphic families of plumbing spaces. This will help us to construct exotic families, or moreover, it helps us to understand the difference between smooth/differential topology and symplectic topology.

  • 5 November 2021 16:00--17:30, Online (Zoom link, Zoom Meeting ID: 869 1428 3587, Passcode: 370665)
    A comparison of two symplectic capacities
    Miguel Pereira (University of Augsburg, Germany)
    This talk is about work in progress. A symplectic manifold is a manifold $M$ equipped with a two form $\omega$ which is closed and nondegenerate. A symplectic capacity is a map from the class of symplectic manifolds to $[0,\infty]$, which satisfies some assumptions. A key idea is that symplectic capacities can obstruct the existence of symplectic embeddings between manifolds. Examples of such capacities are the Lagrangian capacity $c_L$ and the capacities $c_k$ coming from $S^1$-equivariant symplectic homology. It is conjectured that for a Liouville domain $(X,\lambda)$ (a special type of symplectic manifold) we have the inequality $c_L(X,\lambda) \leq \inf_{k \in \mathbb{N}} c_k(X,\lambda)/k$. Our goal with this talk is to present the necessary definitions to understand this statement, a sketch of how the proof should be and if time allows some implications of this statement.

  • 22 October 2021 13:00--15:00, Online (Zoom link, Zoom Meeting ID: 892 4212 0664, Passcode: 380125)
    Legendrians in the boundary of subcritical Stein manifolds and exotic Stein structure
    Youngjin Bae (Incheon National University, Korea)
    Weinstein 4-manifolds can be obtained by attaching critical handles on the boundary of subcritical Stein manifold. We review Ekholm-Ng's recipe of DGA for Legendrians in the boundary of subcritical Stein manifold. As an application, we also construct an exotic Stein structure on 8-dimensional Euclidean space.

  • 6 July 2021 15:00--16:00, Online (Zoom link, Zoom Meeting ID: 876 3033 8265, Passcode: 239559)
    Mirror Symmetry Correspondence between Indecomposable Cohen-Macaulay Modules over Degenerate Cusps and Immersed Lagrangians on Surfaces
    Kyeongmin No (Seoul National University, Korea)
    Burban and Drozd (2017) classified all indecomposable maximal Cohen-Macaulay modules over degenerate cusps. For the degenerate cusp defined by $xyz$, its mirror is given by a pair of pants (Abouzaid, Auroux, Efimov, Katzarkov and Orlov). We find explicit objects in the Fukaya category of a pair of pants, which correspond to every indecomposable Cohen-Macaulay modules in Burban and Drozd's list under the localized mirror functor. This is a joint work in progress with Cheol-Hyun Cho, Wonbo Jeong and Kyoungmo Kim.

  • 29 June 2021 15:00--16:30, Room 8101
    Fukaya categories and Lens spaces
    Sangjin Lee (IBS Center for Geometry and Physics in Pohang, Korea)
    Many of my topologists, but not symplectic topologists, friends asked me a question: what topological information could be provided from Fukaya categories? In this talk, we will see an example answering the question. More precisely, I will introduce an algebraic tool that makes Ganatra-Pardon-Shende's result easier to be applied. With the tool, one could compute the wrapped Fukaya categories of cotangent bundles of Lens spaces, which are equivalent to each other, if two Lens spaces are of the same homotopy type. This talk is based on a joint work in progress with Dogancan Karabas.

  • 22 June 2021 16:00--17:30, Room 1423
    Bruhat interval polytopes and toric varieties of Catalan type
    Eunjeong Lee (IBS Center for Geometry and Physics in Pohang, Korea)
    Bruhat interval polytopes form an interesting family of polytopes lie in the permutohedron, each of which is defined by the convex hull of points associated with permutations $z$ for $v \le z \le w$. A Bruhat interval polytope is the moment polytope of a subvariety of the flag variety, called a Richardson variety, and it is known that the Richardson variety is a smooth toric variety if and only if the Bruhat interval polytope is combinatorially equivalent to a cube. In this talk, we will consider an interesting family of smooth projective toric varieties, called toric varieties of Catalan type. As one may expect, there is a bijective correspondence between the set of toric varieties of Catalan type and that of polygon triangulation. Moreover, we will study the isomorphism classes of toric varieties of Catalan type and how they are related to smooth toric Richardson varieties. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.

  • 11 May 2021 15:00--16:00, Online (Zoom link, Zoom Meeting ID: 828 5833 0695, Passcode: 115128)
    Topological String Theory and S-duality
    Philsang Yoo (YMSC, Tsinghua University, China)
    S-duality is a non-trivial equivalence of two physical theories. The main aim of the talk is to explain how to mathematically understand S-duality in the simple context of topological string theory, or more precisely, a twisted version of type IIB supergravity theory. A large part of the talk will be devoted to providing a dictionary between string theory and mathematical objects. This talk is based on a joint work with Surya Raghavendran.

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

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