Collaborative Research: Illinois-Indiana symplectic geometry conference

“伊利诺斯州-印第安纳州辛几何会议”将分别于2008年春季和2009年秋季在伊利诺伊大学uii分校、圣母大学分校、普渡大学和伊利诺伊大学UIUC分校举行。会议时间很短，在周末举行，通常包括大约六场受邀演讲。这些讲座将大致反映伊利诺斯州和印第安纳州辛拓扑学家及其合作者的兴趣和研究计划。特别地，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；花同源性与深谷范畴；左切茨振动理论；三维接触拓扑；接触同调与辛场论；哈密顿流动力学；通过Seiberg-Witten和heegard - flower理论在低维拓扑中的应用。这些会议将成为该地区讨论和研究交流的中心。在过去的二十年里，辛拓扑已经从一个毫无疑问的基础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的原创和鼓舞人心的结果。它起源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。这一发展已经被主要的数学系所认识，他们已经招募了辛拓扑学家。现在，即使是相对较小的地理区域，如伊利诺伊州和印第安纳州到芝加哥南部和东部的地区，也有几个健康的研究小组。这一建议利用了定期会议的这种情况。会议将把活跃的研究人员、研究生和其他学科的感兴趣的人聚集在一起，在周末的讨论和合作中，邀请该领域的领导者进行讲座。该项目将促进该地区辛几何学者之间的互动，并激发新的想法和研究。

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.