Cornell Topology Festival Support; 2003-2005

Cornell University, Ithaca NY

Investigators

Abstract

Abstract Award: DMS-0244361 Principal Investigator: Peter J. Kahn The topology/geometry group in the Department of Mathematics at Cornell University requests funding to continue support for three years for the Cornell Topology Festival, which this group has hosted each year since 1963. The Festival provides a significant arena for the dissemination and development of important, new results from a wide array of areas within the realms of algebraic, differential, and geometric topology, and allied subjects. While it is planned to continue the broad, interdisciplinary flavor and collaboration-friendly format that have characterized the Festival over the years, it is also proposed to extend the Festival by a day to accommodate specific annual areas of emphasis. In this way the Festival can be responsive to the dominant trends of this era: namely, the simultaneous flourishing of both subspecializations and cross-disciplinary activity. An active outreach program, which includes some travel support, will be initiated to broaden participation in the Festival. For our initial conference under this grant (May 1-4, 2003), we will have as area of emphasis the very active field of geometric group theory. The Topology Festival was conceived and initiated in the 1960's both as an annual celebration of the burgeoning field of topology and as an annual conference/workshop for topologists in the northeastern United States. While topology has deep roots in early European mathematical investigations of space and geometry, it is in the mid-twentieth century that topology came of age, with American mathematicians providing a large array of seminal discoveries. American topology has been a key element in America's world leadership in mathematics. Topology is a broad subject, which overlaps with areas of `discrete' mathematics (e.g., algebra, combinatorics), as well as with `continuous' or `smooth' mathematics (e.g., differential geometry, dynamical systems, mathematical physics). Indeed, a large part of contemporary mathematics has been profoundly affected by topological results and methods. As a foundational subject, the applications of topology are very widespread. A few examples are: genetics (the study of knotting of DNA molecules), neuroscience and robotics (dynamical systems modeling), computer science ( in geometric modeling and simulation), mathematical economics (in smooth equilibrium theory), physics (the theory of gauge fields), and neighboring fields in mathematics (e.g., geometric group theory). Although many of the basic questions that powered early efforts in topology have been answered, new problems are constantly being generated as science moves forward, and important classical problems remain. An example of the latter is the Poincare Conjecture, which has been the subject of several notable talks at past Topology Festivals and remains one of the premier unsolved problems of mathematics today---one of the Clay Institute's seven `millenium problems'--- and the focus of intense research. The topologists and geometers at Cornell are proud of the useful role that the Topology Festival has played and will continue to play in the contemporary development of this dynamic area of mathematics.