The field of topology became an independent mathematical discipline around the turn of the century. Since then, it has grown into a large and diversified area of mathematical activity. Methods from the different subareas of topology have widely influenced current research in many other areas, from mathematical physics to algebra and number theory. The conference supported by this grant will focus on the use of topology in three main areas of current research: Global geometry, topology and mathematical physics (including gauge field theory, topological and conformal quantum field theories, and the global geometry of the Dirac operator); Algebraic geometry and algebraic K-theory; and Dynamical systems. The conference, entitled Topological Methods in Modern Mathematics, will be held at SUNY Stony Brook, June 14-21, 1991. In each of the three areas there will be broad survey talks together with more detailed lectures on the most important and exciting recent developments. The conference will provide an opportunity for mathematicians from three distinct mathematical disciplines whose common feature is the use of topological methods and results to come together and interact in an extremely fruitful way. In addition, special tutorial programs are planned for graduate and undergraduate students, so that they may also participate in the conference and gain a sense of the reality and excitement of research mathematicians.
