The program focuses on relations between physics and topology in low dimensions, where `low' is understood to mean `less than twelve'.

String theory has been concerned with moduli spaces of Riemann surfaces since its inception; the topology of those spaces, and their relations with mapping-class groups and the Mumford conjecture, defines one of the central themes of the conference. Applications of the topology of moduli spaces to the study of four-manifolds is another field of intense activity; from the physical point of view these subjects share many common features, but mathematical understanding of their analogies is less developed, and we hope this conference will promote progress in that direction. Quite recently, the range of applications of topology to quantum field theory has been considerably deepened by developments in the theory of open strings and D-branes, which are also connected to questions of special geometry, theory of derived categories, and noncommutative geometry.

We hope this conference will help create some unity of thinking within this broad research area. Time and other constraints have forced us to background dimension three, but we hope to make up for some of that neglect that in the 2002-3 JAMI program on knots and primes, and other connections between three-manifolds and number fields.