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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.