Collaborative Proposal: Illinois-Indiana Symplectic Geometry

点击翻译按钮获取中文摘要

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.