时间：2025年6月14日
地点：后主楼1124
日程表
09:55-10:00 开幕式
10:00-10:50 李天军（明尼苏达大学）
11:10-12:00 潘宇（天津大学）
14:00-14:50 高原（南京大学）
15:10-16:00 张俊（中国科学技术大学）
16:20-17:10 吴惟为（浙江大学）
题目和摘要
Speaker: 李天军（明尼苏达大学）
Title: Symplectic log Kodaira dimension −∞, affine-ruledness and unicuspidal rational curves
Abstract: A classical theorem of Liu-Ohta-Ono asserts that any symplectic 4-manifold with negative pairing between the symplectic form and canonical class must be rational or ruled. This result is a symplectic reminiscence of the more classical characterization of complex surfaces with Kodaira dimension −∞. In this talk, we will discuss the generalization of Liu-Ohta-Ono’s theorem to the relative setting by considering symplectic divisors whose adjoint class has negative pairing with canonical class. In parallel to the theorem of Fujita-Miyanishi-Sugie-Russell in the algebraic context, we show that the complement of such divisors is foliated by a certain family of unicuspidal rational curves, thereby admitting the affine-ruled structure. This is based on joint work with Shengzhen Ning.
Speaker: 潘宇（天津大学）
Title: Reverse Lagrangian surgeries
Abstract: A major theme in symplectic and contact topology is the study of Legendrian knots and exact Lagrangian surfaces. In the talk, we will talk about some flexibility results of immersed Lagrangian surfaces using augmentation, a Floer type invariant of Legendrian knots. In particular, for an immersed filling of a topological knot, one can do surgery to resolve a double point with the price of increasing the surface genus by 1. In the Lagrangian analog, one can do Lagrangian surgery on immersed Lagrangian fillings to treat a double point by a genus. In this talk, we will explore the possibility of reversing the Lagrangian surgery, i.e., compressing a genus into a double point. It turns out that not all Lagrangian surgery is reversible.
Speaker: 高原（南京大学）
Title: Categorical residues and duality
Abstract: Various types of duality results in both symplectic and algebraic geometry are well-known to be related to Calabi-Yau structures on the relevant categories. In this talk, I'll discuss an abstract approach, closely related to Beilinson-Tate residue theory, to provide ingredients for constructing Calabi-Yau structures on dg/A-infinity categories that are not necessarily proper. Applications include duality type results for Rabinowitz Fukaya categories, singularity categories, and so on.
Speaker: 张俊（中国科学技术大学）
Title: Distinguish submanifolds via spectral capacities
Abstract: In this talk, we will explore the measurement of submanifold sizes within symplectic manifolds using symplectic invariants derived from spectral data in (Hamiltonian) Floer theory. These invariants serve as concrete realizations of spectral capacities. By employing these capacities, we will elucidate a fundamental distinction between Lagrangian submanifolds and symplectic submanifolds (or, more generally, nowhere coisotropic submanifolds).
Additionally, we will present a novel quantitative Lagrangian control estimate that reveals unexpected relationships among these invariants. This talk is based on joint work with Dylan Cant.
Speaker: 吴惟为（浙江大学）
Title: Symplectic Torelli groups of log Calabi-Yau surfaces
Abstract: The symplectic Torelli group of a symplectic manifold is formed by homotopy classes of homologically trivial symplectomorphisms. For log Calabi-Yau surfaces, such symplectomorphisms have the trivial smooth isotopy class, hence the symplectic Torelli group exactly captures the exotic symplectomorphisms. A question of Donaldson asks whether Lagrangian Dehn twists generate symplectic Torelli groups. In this talk, weexplain how to compute the symplectic Torelli group for all but three symplectic surfaces which support log Calabi-Yau structures. This leads to an affirmative answer to Donaldson's question and proves that all toric surfaces have trivial symplectic Torelli groups. As a by-product, we show the existence of a Hamiltonian Z/2-action on a symplectic four manifold which does not extend to an S^1-action. This is joint work with Tian-Jun Li and Jun Li.
会议组织：田垠（yintian@bnu.edu.cn）程志云（czy@bnu.edu.cn）
会议资助：NSFC12471064，NSFC12371065
