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Klappentext Visionary articles explaining approaches to important problems on the interface of pure mathematics and mathematical physics. Zusammenfassung These proceedings contain surveys articles! research articles! and visionary articles that explain new approaches to important problems on the interface of pure mathematics and mathematical physics. Ideal for students and researchers! it gives a snapshot of the state of the field as well as defining directions for future research. Inhaltsverzeichnis 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.
