L3 Graduate Student Workshop in Symplectic/Contact Geometry

L3 辛/接触几何研究生研讨会

• 批准号: 1619754
• 负责人: Emmy Murphy
• 金额: $ 0.49万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619754&HistoricalAwards=false
• 关键词: L3; Graduate; Student; Workshop; Symplectic

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.

该奖项支持为期一周的研讨会，题为“L3研究生辛/接触几何研讨会”，在新奥尔良举行，路易斯安那州，在2016年1月19日至23日。 辛几何是一个领域，连接几个研究领域，如数学物理，几何拓扑，代数几何，镜像对称和弦理论。 本次研讨会的目的是向与会者介绍当代研究和讨论未来的方向。 研究生将提供大部分的演讲。该研讨会可能作为一个试点，为辛拓扑和几何的学生未来的年度活动。研讨会的重点是探索之间的联系温斯坦流形和接触几何，与莱夫谢茨纤维化和代数几何。Weinstein流形是辛几何和镜像对称的中心研究对象。 它们通常被赋予Lefschetz纤维化的结构，它用一个少一维的Weinstein流形的拉格朗日子流形来描述它们的几何，或者，人们可以用接触流形中的勒让德子流形来描述它们的几何。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取消，并使计算的组合更容易。 研讨会将开始与理论的基本对象和工具的讨论，并与当前的研究和新的方向结束。 研讨会的网页是http://math.stanford.edu/~ksiegel/workshop/main.html。