Collaborative Proposal: Illinois-Indiana Symplectic Geometry

合作提案：伊利诺伊州-印第安纳州辛几何

• 批准号: 0757762
• 负责人: Ely Kerman
• 金额: --
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0757762&HistoricalAwards=false
• 关键词: Collaborative; Proposal; Illinois; Indiana; Symplectic

An "Illinois-Indiana symplectic geometry conference" will take place in the spring and then fall of 2008 and 2009 at IUPUI, Notre Dame, Purdue and UIUC universities respectively. The conferences will be short, held over a weekend, and typically include around six invited lectures. These lectures will generally reflect the interests and research plans of symplectic topologists, and their collaborators, in Illinois and Indiana. In particular, lecture topics will include, but not be limited to, the following branches of symplectic topology: the theory of holomorphic curves and Gromov-Witten theory; Floer homology and Fukaya categories; the theory of Leftschetz fibrations; three-dimensional contact topology; contact homology and symplectic field theory; dynamics of Hamiltonian flows; applications to low dimensional topology via Seiberg-Witten and Heegard-Floer theory. The meetings will become centers of discussion and research communication in the region.Over the past twenty years symplectic topology has evolved from an undoubtedly fundamental yet prohibitively intractable field into one of the most popular and exciting areas of mathematical research, producing a constant stream of deeply original and inspiring results. Its origins lie in classical and quantum mechanics but the subject is now closely tied to many areas of mathematics and theoretical physics, not least complex analysis, smooth topology, partial differential equations and mirror symmetry.This development has been recognized by major math departments which have recruited symplectic topologists. Now even relatively small geographical areas, such as the regions of Illinois and Indiana to the south and east of Chicago, are home to several healthy groups of researchers. This proposal exploits this circumstance with a regular conference. The meetings will bring together active researchers, graduate students and interested people from other disciplines for a weekend of discussion and collaboration centered around lectures from invited leaders in the field. The project will foster interaction amongst symplectic geometers in the region and stimulate new ideas and research.

一个“伊利诺斯州印第安纳辛几何会议”将于2008年春季和2009年秋季分别在IUPUI、圣母大学、普渡大学和UIUC大学举行。会议将很短，在一个周末举行，通常包括大约六个邀请讲座。这些讲座将普遍反映利益和辛拓扑学家的研究计划，以及他们的合作者，在伊利诺伊州和印第安纳州。特别是，讲座主题将包括，但不限于，辛拓扑的以下分支：全纯曲线理论和Gromov-Witten理论; Floer同调和福谷范畴; Leftschetz纤维化理论;三维接触拓扑;接触同调和辛场论;动力学的哈密顿流;应用到低维拓扑通过Seiberg-Witten和Heegard-Floer理论。这些会议将成为该地区的讨论和研究交流中心。在过去的二十年中，辛拓扑已经从一个毫无疑问的基本但令人望而却步的棘手领域发展成为数学研究中最受欢迎和最令人兴奋的领域之一，产生了源源不断的深刻原创和鼓舞人心的结果。它的起源在于经典力学和量子力学，但这门学科现在与数学和理论物理的许多领域密切相关，尤其是复杂分析，光滑拓扑，偏微分方程和镜像对称。这一发展已被各大数学系所认可，这些系已经招募了辛拓扑学家。现在，即使是相对较小的地理区域，如芝加哥以南和以东的伊利诺伊州和印第安纳州，也有几个健康的研究小组。这项建议利用了这一情况，定期举行会议。这些会议将汇集活跃的研究人员，研究生和其他学科的感兴趣的人，围绕该领域受邀领导人的讲座进行周末的讨论和合作。该项目将促进该地区辛几何学家之间的互动，并激发新的想法和研究。