KIAS Topology Seminar
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, and Jongbaek Song.
Schedule, Year 2021
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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