Title and abstract

Yunhyung Cho (Sungkyunkwan University)

Monotone Lagrangian tori via toric degeneration I

In this talk, I will explain a method of obtaining a family of monotone Lagrangian tori in a smooth Fano variety via toric degeneration. Our method is particularly useful when our variety is birational to a cluster variety such as a (partial) flag variety. Using our machinery, we obtain a family of infinitely many monotone Lagrangian tori in a full flag manifold. We also discuss how to generalize our machinery to an arbitrary Fano case. This is joint / partly joint work with Yoosik Kim, Myungho Kim, and Euiyong Park.

Sung Rak Choi (Yonsei University)

On the existence of anti-minimal model

Due to the recent remarkable development of the minimal model program, it is known that there exist minimal models when the canonical divisor is big or effective in some occasions. In this talk, we report some recent progress on the existence of the anti-minimal model. The so-called anti-minimal model program does not run easily mainly because the classical results for the usual MMP fail to hold once we replace the canonical divisor with the anticanonical divisor. We will also try to explain how we can overcome the difficulties.

Morimichi Kawasaki (Hokkaido University)

Relative simplicity of the universal coverings of transformation groups

Many transformation groups on manifolds are simple, but their universal coverings are not. In this talk, we introduce the concept of the relative simplicity of groups instead of the simplicity of groups. We show that the universal coverings of many transformation groups (including the group of Hamiltonian diffeomorphisms) are relatively simple and we provide some applications. We note that one of the motivations of this study is symplectic geometry. This is a joint work with Mitsuaki Kimura (Osaka Dental University), Yoshifumi Matsuda (Aoyama Gakuin University), Takahiro Matsushita (Shinshu University), Ryuma Orita (Niigata University).

Yoosik Kim (Pusan National University)

Monotone Lagrangian tori via toric degeneration II

This talk is a continuation of Yunhyung's talk. I will explain a method of obtaining a family of monotone Lagrangian tori in a smooth Fano variety via toric degeneration. Our method is particularly useful when our variety is birational to a cluster variety such as a (partial) flag variety. Using our machinery, we obtain a family of infinitely many monotone Lagrangian tori in a full flag manifold. We also discuss how to generalize our machinery to an arbitrary Fano case. This is joint / partly joint work with Yunhyung Cho, Myungho Kim, and Euiyong Park.

Eunjeong Lee (Chungbuk National University)

An exploration of torus orbit closures

A flag variety is a smooth projective homogeneous variety, denoted as G/B, where G is a semisimple Lie group and B is a Borel subgroup. The maximal torus T⊂B acts on G/B via left multiplication. Considering the closures of torus orbits under this T-action, one can construct a family of toric varieties within G/B. For example, a permutohedral variety can be obtained in this manner. In this talk, we will explore these toric varieties. This talk is based on joint work with Sujin Cho and Jaehyun Hong, as well as several collaborations with Seonjeong Park and Masuda.

Kyoung-Seog Lee (POSTECH)

Symmetric products, Jacobians and moduli spaces of vector bundles of algebraic curves

Symmetric products, Jacobians and moduli spaces of vector bundles on curves are fundamental objects in the study of algebraic curves. In this talk, I will explain how they are related in the level of their derived categories and motives. This talk is based on several joint works with I. Biswas, T. Gomez, H.-B. Moon and M. S. Narasimhan.

Changzheng Li (Sun Yat-Sen University)

A Plucker coordinate mirror for partial flag varieties and quantum Schubert calculus

In this talk, we will review the current study of mirror symmetry for flag varieties. We will focus more on the construction of the Landau-Ginzburg model, and discuss a folklore mirror symmetry expectation on the eigenvalues of the first Chern class, using concrete examples of flag varieties of Lie type A. This is based on a work-in-progress joint with Konstanze Rietsch, Mingzhi Yang, and Chi Zhang.

Yat-Hin Suen (National Cheng Kung University)

Cluster structure on the moduli space of toric vector bundles over toric surfaces

We use spectral networks and non-abelianization to construct toric vector bundles over toric surfaces and prove that the moduli space of rank 2 toric vector bundles over any complete toric surface admits a cluster structure.

Rui Wang (University of California, Berkeley)

My Journey of Mathematics after IBS-CGP

In this talk, I will describe my mathematical work over the past 10 years, which coincides with the time since I left Pohang. This includes research on Hamiltonian Gromov–Witten theory, orbifold Gromov–Witten theory, as well as reflections on my approach to mathematical education, drawing on knowledge and experiences from my time in Pohang.

Hwajong Yoo (Seoul National University)

Rational torsion points on Jacobian varieties

We introduce a famous conjecture of Andrew Ogg, which was proved by Mazur, and discuss its generalization.

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