------ Fall 2000 ------
The program ``Low-dimensional contact geometry" is organized jointly by the American Institute of Mathematics (AIM) and the Department of Mathematics of Stanford University. It will run from mid-August till mid-December 2000. The program will end with a a Contact Geometry Workshop. The goal of the program is to capitalize on recent progress in contact geometry. It seems that the time is ripe now for new breakthroughs in the field, and that the concentration of both established 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 transversal knots in contact 3-manifolds, and to establish further properties of contact 3-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, including non-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 a number 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.