Titles and Abstracts

문지연

Title: The real Delzant construction in symplectic toric manifolds

Abstract: A real Lagrangian submanifold of a symplectic toric manifold M is given by the fixed point set of an anti-symplectic involution on it. If the involution is standard, then the real Lagrangian is a real toric manifold. To obtain nontrivial anti-symplectic involutions, we shall lift a symmetry of the Delzant polytope of M to an anti-symplectic involution on M. This will be useful to study the topology of real Lagrangians. This is an ongoing project with Joé Brendel and Joontae Kim.

최수영

Title: On the real toric spaces

Abstract: In the lectures, I would like to introduce recent achievements on the real toric spaces. The topology and combinatorics of real toric spaces will be presented. In addition, I will introduce a rough plan for building up the database of small covers.

오정석

Title: Virtual cycles

Abstract: We explain the virtual cycles in terms of Euler classes. And we discuss the definition of Gromov-Witten invariants.

박선정

Title: Torus orbit closures in the flag variety

Abstract: The flag variety $\mathcal{F}\ell_n$ has an action of the torus $T=(\mathbb{C}^\ast)^n$ and the closure of the $T$-orbit of a generic point of $\mathcal{F}\ell_n$ is the smooth toric variety defined by the normal fan of the permutohedron of dimension $n-1$.

In this talk, we will discuss the $T$-orbit closures of the flag variety. This talk is based on joint work with Eunjeong Lee and Mikiya Masuda in progress.

송종백

Title: Equivariant cohomology algebras of good contact toric manifolds.

Abstract: We discuss a topological generalization of good contact toric manifolds and study their equivariant cohomology algebras.

이기녕

Title: TBA

Abstract: TBA

이은정

Title: Gelfand--Cetlin type string polytopes

Abstract: Let $G$ be a simply-connected reductive algebraic group over $\mathbb{C}$. For a reduced decomposition $\mathbf{i}$ of the longest element of the Weyl group of $G$ and a dominant integral weight $\lambda$, one can define the string polytope $\Delta_{\mathbf i}(\lambda)$. The string polytope $\Delta_{\mathbf i}(\lambda)$ encodes weights of the $G$-irreducible representation of highest weight $\lambda$. It has been observed that the combinatorics of string polytopes depend on a choice of $\lambda$.

In this talk, we introduce a description of string polytopes when $G$ is the special linear group $\textrm{SL}_{n+1}(\mathbb{C})$, and study a necessary and sufficient condition on $\mathbf i$ such that the string polytope $\Delta_{\mathbf i}(\lambda)$ is unimodularly equivalent to the Gelfand--Cetlin polytope, which is the most well-known string polytope, for a regular dominant weight $\lambda$.

This talk is based on joint work with Yunhyung Cho, Yoosik Kim, and Kyeong-Dong Park.

황택규

Title: Symplectic homology and capacities

Abstract: A symplectic capacity is a quantity that measures the "size" of symplectic manifolds. The goal of this talk is to review the construction of symplectic capacities by Gutt and Hutchings. I will explain how the capacities are related to symplectic homology and describe computations for toric domains.