Cornell Topology Festival Support; 2003-2005

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AbstractAward: DMS-0244361Principal Investigator: Peter J. KahnThe topology/geometry group in the Department of Mathematics atCornell University requests funding to continue support for threeyears for the Cornell Topology Festival, which this group hashosted each year since 1963. The Festival provides a significantarena for the dissemination and development of important, newresults from a wide array of areas within the realms ofalgebraic, differential, and geometric topology, and alliedsubjects. While it is planned to continue the broad,interdisciplinary flavor and collaboration-friendly format thathave characterized the Festival over the years, it is alsoproposed to extend the Festival by a day to accommodate specificannual areas of emphasis. In this way the Festival can beresponsive to the dominant trends of this era: namely, thesimultaneous flourishing of both subspecializations andcross-disciplinary activity. An active outreach program, whichincludes some travel support, will be initiated to broadenparticipation in the Festival. For our initial conference underthis grant (May 1-4, 2003), we will have as area of emphasis thevery active field of geometric group theory.The Topology Festival was conceived and initiated in the 1960'sboth as an annual celebration of the burgeoning field of topologyand as an annual conference/workshop for topologists in thenortheastern United States. While topology has deep roots inearly 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 seminaldiscoveries. American topology has been a key element inAmerica's world leadership in mathematics. Topology is a broadsubject, which overlaps with areas of `discrete' mathematics(e.g., algebra, combinatorics), as well as with `continuous' or`smooth' mathematics (e.g., differential geometry, dynamicalsystems, mathematical physics). Indeed, a large part ofcontemporary mathematics has been profoundly affected bytopological results and methods. As a foundational subject, theapplications of topology are very widespread. A few examples are:genetics (the study of knotting of DNA molecules), neuroscienceand robotics (dynamical systems modeling), computer science ( ingeometric modeling and simulation), mathematical economics (insmooth equilibrium theory), physics (the theory of gauge fields),and neighboring fields in mathematics (e.g., geometric grouptheory). Although many of the basic questions that powered earlyefforts in topology have been answered, new problems areconstantly being generated as science moves forward, andimportant classical problems remain. An example of the latter isthe Poincare Conjecture, which has been the subject of severalnotable talks at past Topology Festivals and remains one of thepremier unsolved problems of mathematics today---one of the ClayInstitute's seven `millenium problems'--- and the focus ofintense research. The topologists and geometers at Cornell areproud of the useful role that the Topology Festival has playedand will continue to play in the contemporary development of thisdynamic area of mathematics.