09:00-10:00

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田志宇

刘治宇

10:00-10:30

茶歇

茶歇

10:30-11:30

李思

范佑维

11:30-14:00

午餐

午餐

14:00-15:00

方博汉

李展

离会

15:00-15:30

茶歇

茶歇

15:30-16:30

李长征

曹亚龙

18:00

晚餐

范祐维

Title: Gepner points in the Kahler moduli of K3 surfaces

Abstract: In this talk, we will discuss a classification of finite subgroups of the group of autoequivalences of the derived category of coherent sheaves on a general K3 surface. We will provide the necessary background on Bridgeland stability conditions and mirror symmetry. Joint work with Kuan-Wen Lai.

方博汉

Title: Remodeling conjecture with descendants

Abstract: For a toric Calabi–Yau threefold, I will explain the correspondence between an equivariant line bundle supported on a toric subvariety and a relative homology cycle on the covering space of the mirror curve. The Laplace transform of the holomorphic Liouville form along this cycle gives genus-zero descendant Gromov–Witten invariants with a certain Gamma class of that bundle. Hence, the Laplace transform of the topological recursion produces all-genus descendant Gromov–Witten invariants with Gamma classes. This talk is based on ongoing joint work with Melissa Liu, Song Yu, and Zhengyu Zong.

李长征

Title: Mirror symmetry for certain blowup of Grassmannians 

Abstract: In this talk, we will discuss the Fano property of the blowup of a complex Grassmannian Gr(k, n) along a sub-Grassmannian Gr(r, m). We will study the quantum cohomology when (r, m)=(k, n-1), and will further discuss the mirror symmetry when k=2. This is based on my work in progress joint with Jianxun Hu, Huazhong Ke and Lei Song.

李思

Title: Homological Method in Topological/Holomorphic QFT

Abstract:We discuss basic ideas and various recent mathematical developments about quantization that arises from topologically/holomorphically twisted quantum field theory. We illustrate some applications in topological/chiral algebraic index, topological B-model and mirror symmetry.

李展

Title: Recent developments on the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces

Abstract: A fibration with a relatively trivial canonical divisor is called a Calabi-Yau fiber space. The Morrison-Kawamata cone conjecture relates the birational geometry of a Calabi-Yau fiber space to the convex geometry of a movable cone. I will report on recent developments regarding the Morrison-Kawamata cone conjecture and possible further directions.

刘治宇

Title: A new deformation type of irreducible symplectic varieties

Abstract: Irreducible symplectic varieties are one of three building blocks of varieties with Kodaira dimension zero, which are higher-dimensional analogs of K3 surfaces. Despite their rich geometry, there have not been many known approaches to construct irreducible symplectic varieties. In this talk, I will introduce a general criterion for the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations, based on the minimal model program and the geometry of general fibers. As an application, I will explain how to get a 42-dimensional irreducible symplectic variety with the second Betti number at least 24, which belongs to a new deformation type. This is a joint work with Yuchen Liu and Chenyang Xu.

田志宇

Title: Space of rational curves: conjecture and examples

Abstract: In the first part of the talk, I will discuss some conjectures about the asymptotic behavior of the space of rational curves on a rationally connected varieties. While the conjectures are open in general, there are interesting cases where one can verify some of the conjectures, which will be discussed in the second part of the talk.