The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

• Contains Segal's influential paper on The Definition of Conformal Field Theory published for the first time • Articles from contributors of the highest possible calibre • Truly interdisciplinary subject matter

### Contents

Part I. Contributions: 1. A variant of K-theory Michael Atiyah and Michael Hopkins; 2. Two-vector bundles and forms of elliptic cohomology Nils Baas, Bjorn Dundas and John Rognes; 3. Geometric realisation of the Segal-Sugawara construction David Ben-Zvi and Edward Frenkel; 4. Differential isomorphism and equivalence of algebraic varieties Yuri Berest and George Wilson; 5. A polarized view of string topology Ralph Cohen and Veronique Godin; 6. Random matrices and Calabi-Yau geometry Robbert Dijkgraaf; 7. A survey of the topological properties of symplectomorphism groups Dusa McDuff; 8. K-theory from a physical perspective Gregory Moore; 9. Heisenberg groups and algebraic topology Jack Morava; 10. What is an elliptic object? Stephan Stolz and Peter Teichner; 11. Open and closed string field theory interpreted in classical algebraic topology Dennis Sullivan; 12. K-theory of the moduli of principal bundles on a surface and deformations of the Verlinde algebra Constantin Teleman; 13. Cohomology of the stable mapping class group Michael S. Weiss; 14. Conformal field theory in four and six dimensions Edward Witten; Part II. The Definition of Conformal Field Theory by Graeme Segal: 15. Definition of a conformal field theory Graeme Segal.