Conference: Topological and Quantitative Aspects of Symplectic Manifolds; Columbia University and Barnard College, March 17-20, 2016

该补助金的目的是支持大约27初级参与者，主要是研究生和博士后研究员，在会议上“辛流形的拓扑和定量方面”将于2016年3月17日至20日在哥伦比亚大学和巴纳德学院举行。会议将由穆罕默德·阿布扎伊德、艾尔莎·基廷、罗伯特·利普希茨、沃尔特·诺依曼和丽莎·特雷诺组织。会议将有16-20场演讲和大约80名与会者。辛几何和接触几何是经典力学的抽象背景。辛几何最初是为了研究经典力学的哈密顿公式而发展起来的，特别关注天体力学。最近，人们发现辛几何和接触几何是理论高能物理中基本问题的关键，是弦理论的关键组成部分，与规范理论有着密切的关系。粗略地说，辛流形是一个光滑的空间，其中有一个明确定义的面积概念-但不一定是一个明确定义的距离概念。一个关键问题是如何判断两个辛流形是否相同，并列出所有具有某些性质的辛流形。另一个重要的主题是辛流形的大小概念，因为没有距离的内在概念。这个问题特别微妙--例如，一个无限长的圆柱体可能并不比一个有限长的圆柱体在辛意义上更大--这一问题又一次反映在物理学中奇怪的理论现象中。辛几何和大多数数学中的另一个重要话题是对称性：辛空间可以有什么对称性？是否有可能对所有高度对称的辛空间进行分类？最后一个主题是使用光滑辛空间来研究奇异空间：光滑空间更容易分析，但理解它们反映的奇异性是微妙的。本次会议将汇集大约80名研究人员在这些主题，特别强调最近的发展和年轻研究人员的工作，交流思想和成果，这些基础研究课题。当然，最终目标是促进科学的进步。第二个目标是突出女性对该领域的许多贡献，为刚刚起步的女性研究人员提供指导和支持，从而促进数学研究人员的多样性。math.columbia.edu/mcduff70

The purpose of this grant is to support roughly 27 junior participants, primarily graduate students and postdoctoral fellows, at the conference "Topological and quantitative aspects of symplectic manifolds" to be held at Columbia University and Barnard College on March 17-20, 2016. The conference will be organized by Mohammed Abouzaid, Ailsa Keating, Robert Lipshitz, Walter Neumann, and Lisa Traynor. The conference will feature 16-20 talks and roughly 80 participants.Symplectic geometry and contact geometry are the abstract setting of classical mechanics. Symplectic geometry was originally developed to study the Hamiltonian formulation of classical mechanics, with a particular focus on celestial mechanics. More recently, it has turned out that symplectic and contact geometry are key to fundamental questions in theoretical high energy physics, as a key component in string theory and with close relations to gauge theory. Roughly speaking, a symplectic manifold is a smooth space in which there is a well-defined notion of area - but not necessarily a well-defined notion of distance. One key question is how to tell if two symplectic manifolds are the same, and to list all symplectic manifolds with certain properties. Another important topic is the notion of size in symplectic manifolds, given that there is no intrinsic notion of distance. This problem is particularly subtle - it turns out, for instance, that an infinite cylinder may not be symplectically bigger than a finite one - and again is reflected in strange theoretical phenomena in physics. Another important topic in symplectic geometry - and most of mathematics - is symmetry: what symmetries can symplectic spaces have? Is it possible to classify all highly-symmetric symplectic spaces? A last theme is using smooth symplectic spaces to study singular spaces: smooth spaces are easier to analyze, but understanding what properties of singularities they reflect is subtle. This conference will bring together roughly 80 researchers on these topics, with a particular emphasis on recent developments and work by younger researchers, to exchange ideas and results on these basic research topics. The ultimate goal, naturally, is to promote the progress of science. A secondary goal is to highlight the many contributions of women to the field, to provide mentoring and support for women researchers who are just getting started and so promote diversity among mathematics researchers.The conference web page, with information about speakers and registration, ishttp://math.columbia.edu/mcduff70