L3 Graduate Student Workshop in Symplectic/Contact Geometry

该奖项支持于2016年1月19-23日在路易斯安那州新奥尔良举办的为期一周的工作坊，名为“辛几何/接触几何的L3研究生工作坊”。辛几何是一个连接数学物理、几何拓扑、代数几何、镜像对称和弦理论等多个研究领域的领域。本次研讨会的目标是向参与者介绍当代研究，并讨论未来的方向。研究生将发表大部分演讲。这个工作坊可以作为未来辛拓扑和几何学生年度活动的试点。工作坊的重点是探索Weinstein流形和接触几何之间的联系，以及Lefschetz纤颤和代数几何。Weinstein流形是辛几何和镜像对称性研究的中心对象。它们通常被赋予Lefschetz纤颤的结构，这种结构用一维Weinstein流形的拉格朗日子流形来描述它们的几何。或者，我们可以用接触流形中的Legendrian子流形来描述几何。由于接触几何通常更灵活，这允许我们进行一些额外的几何抵消，并使计算的组合更容易。研讨会将以理论中的基本对象和工具的讨论开始，以当前的研究和新的方向结束。工作坊的网页为http://math.stanford.edu/~ksiegel/workshop/main.html.

This award supports a week long workshop, titled "L3 Graduate Student Workshop in Symplectic/Contact Geometry," held at New Orleans, Louisiana, on January 19-23, 2016. Symplectic Geometry is a field that connects several research areas such as mathematical physics, geometric topology, algebraic geometry, mirror symmetry and string theory. The goal of this workshop is to introduce participants to contemporary research and discuss future directions. Graduate students will give the majority of the talks. The workshop may serve as a pilot for a future annual event for students of symplectic topology and geometry.The focus of the workshop is exploring connections between Weinstein manifolds and contact geometry, with Lefschetz fibrations and algebraic geometry. Weinstein manifolds are central objects of study in symplectic geometry and mirror symmetry. They are often given the structure of Lefschetz fibrations, which describes their geometry in terms of Lagrangian submanifolds of a Weinstein manifold of one dimension less. Alternatively, one can describe the geometry in terms of Legendrian submanifolds in a contact manifold. As contact geometry is generally more flexible, this allows us to make a number of additional geometric cancellations and makes the combinatorics of the computations easier. The workshop will begin with a discussion of the essential objects and tools in the theory, and end with current research and new directions. The workshop webpage is at http://math.stanford.edu/~ksiegel/workshop/main.html.