Symplectic solvmanifolds and their friends

辛几何是经典力学和量子理论的数学基础。物理系统的对称群决定了支配其行为的守恒定律。这个项目的目的是促进对一大类这样的对称群及其相关的辛几何的理解，这些几何被称为辛解流形。这个项目的目的是：确定编码在基本群中的辛解流形的拓扑性质；它们以完整群的形式的几何性质；以及它们的辛代数的代数性质。该项目致力于对辛几何的构件进行分类。

Symplectic geometry is the mathematical foundation of classical mechanics and quantum theory. The symmetry group of a physical system determines the conservation laws governing its behaviour. This project aims to advance the understanding of a large class of these symmetry groups and their associated symplectic geometries, which are called symplectic solvmanifolds. The project aims to: determine the topological properties of symplectic solvmanifolds as encoded in their fundamental groups; their geometric properties in the form of holonomy groups; and the algebraic properties of their symplectic algebras. The project endeavours to classify the building blocks of symplectic geometry.