Workshop on Low-Dimensional Contact Geometry

建议：DMS-0075477PI：Yakov eliashberg等人摘要：低维接触几何计划是由美国数学研究所(AIM)和斯坦福大学数学系联合组织的。它将从2000年8月中旬持续到12月中旬。该计划将以AA联系几何研讨会结束。该计划的目标是利用接触几何方面的最新进展。现在看来，在这一领域取得新突破的时机已经成熟，集中接触和辛几何及其相关领域的成熟和年轻的研究人员，以及几个研究生的参与，可能有助于产生新的显著结果。组织者认为，三维接触几何的连贯图景是指日可待的。特别是，与会者将努力实现对大类三维流形的接触结构的完整分类，进一步发展接触三维流形中的勒让德和横截结理论，并建立作为辛四维流形边界的接触三维流形的进一步性质。接触几何诞生于两个多世纪前惠更斯、汉密尔顿、雅各比的工作中，作为光学的几何语言。人们很快意识到，它在许多其他领域也有应用，包括非完整力学和热力学。在日常生活中，当停车、滑冰、使用冰箱或观看一杯水中美丽的光线游戏时，人们都会遇到接触几何。索菲斯·李、伊利·卡坦、达布和许多其他伟大的数学家都为这一课题付出了大量的努力。然而，直到最近，大多数结果都是地方性的。随着八十年代辛拓扑和接触拓扑学的诞生，这一学科重生，在过去的十年里见证了许多突破性的发现。发现了与哈密顿力学、辛几何和次黎曼几何、分层理论、复杂几何和分析、拓扑流体力学、三维拓扑学和纽结理论的新的重要相互作用。该程序的详细信息可在http：/math.stanford.edu/contact.html上找到

Proposal: DMS-0075477PI: Yakov eliashberg et alAbstract:The program ``Low-dimensional contact geometry" is organized jointlyby the American Institute of Mathematics (AIM) and the Departmentof Mathematics of Stanford University. It will run frommid-August till mid-December 2000. The program will end with aa Contact Geometry Workshop. The goal of the program is to capitalize on recent progress in contact geometry. It seems that the time is ripe nowfor new breakthroughs in the field, and that the concentration of bothestablished and young researchers in contact and symplectic geometry and related areas, as well as participation of several graduate students, may help to produce new remarkable results. The organizers feel that a coherent picture of contact geometry in 3 dimensions is within reach.In particular, the participants will try to achieve a complete classification of contact structures for large classes of 3-manifolds, to make further advances in the theory of Legendrian and transversalknots in contact 3-manifolds, and to establish further properties of contact3-manifolds which serve as boundaries of symplectic 4-manifolds.Contact geometry was born more than two centuries ago in the work of Huygens, Hamilton, Jacobi as a geometric language for optics. It was soon realized that it has applications in many other areas, includingnon-holonomic mechanics and thermodynamics. One encounters contact geometry in everyday life when parking a car, skating, using a refrigerator, or watching the beautiful play of light in a glass of water. Sophus Lie, Elie Cartan, Darboux and many other great mathematicians devoted a lot of their work to this subject. However, till very recently most of the results were of a local nature. With the birth of symplectic and contact topology in the Eighties, the subject was reborn, and the last decade witnessed anumber of breakthrough discoveries. There were found new important interactions with Hamiltonian mechanics, symplectic and sub-Riemannian geometry, foliation theory, complex geometry and analysis, topological hydrodynamics, 3-dimensional topology, and knot theory.Details of the program can be found at http:/math.stanford.edu/contact.html