Workshop on Low-Dimensional Contact Geometry

提案：DMS-0075477 PI：Yakov eliashberg et al摘要：“低维接触几何”是由美国数学研究所（AIM）和斯坦福大学数学系联合组织的。 研讨会将于2000年8月中旬至12月中旬举行。该计划将结束与aaa接触几何研讨会.该计划的目标是利用接触几何学的最新进展。看来，现在的时机已经成熟，在该领域的新突破，并在接触和辛几何及相关领域，以及几个研究生的参与，bothestablished和年轻的研究人员的浓度，可能有助于产生新的显着成果。 组织者认为，在三维接触几何的连贯图片是触手可及的。特别是，与会者将试图实现一个完整的分类接触结构的大类3-流形，使进一步的发展理论的勒让德和transversknots在接触3-流形，接触几何诞生于两个多世纪前惠更斯，汉密尔顿，雅可比是光学的几何语言。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。人们在日常生活中遇到接触几何时，停车，滑冰，使用冰箱，或观看美丽的光在一杯水中玩耍。Sophus Lie，Elie Cartan，Darboux和其他许多伟大的数学家都致力于这个问题。然而，直到最近，大多数结果都是地方性的。随着80年代辛拓扑和接触拓扑的诞生，这门学科获得了新生，在过去的十年里出现了许多突破性的发现。发现了新的重要的相互作用与哈密顿力学，辛和亚黎曼几何，叶理理论，复杂的几何和分析，拓扑流体力学，三维拓扑，和纽结理论。math.stanford.edu/contact.html

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