讨论类型：数学前沿论坛

主办：天津师范大学yh86银河国际官方网站

报告时间：

2025年3月18号（周二）下午14:00-15:00

2025年3月19号（周三）下午14:00-15:00

2025年3月20号（周四）上午9:00-10:00

报告地点：博理楼B区108

报告题目：Floer homologies and real symplectic capacities

报告人：高蓁 博士

报告人简介:

高蓁，德国奥格斯堡大学博士。师从著名数学家Urs Frauenfelder教授，研究方向为辛几何和弦拓扑。

报告摘要:

Symplectic manifolds are sometimes provided with real symmetries (i.e. anti-symplectic involutions), in which the symplectic geometry and dynamics with respect to the symmetries are studied, e.g. Arnold-Givental conjecture, existence of brake orbits, real symplectic embeddings, etc. Important quantities like symplectic capacities with respect to the real symmetries can be introduced for such investigations. Various constructions through variational calculus perspectives have been implemented by Liu-Wang and Jing-Lu. The goal of this series of talks is to relate these notions to the symplectic capacities extracted from some Floer homologies, hence showing some bounding result. I will first review the Floer theory for the scope of study, e.g. Lagrangian Floer homology, wrapped Floer homology, symplectic homology, and how to construct symplectic capacities out of them. Afterwards, we will delve into the finiteness problem of the real symplectic capacities via the Floer theoretical method.