Topology, Geometry and Quantum Field Theory: Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal (London ... Lecture Note Series, Series Number 308)

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. This Volume Covers The Proceedings Of An International Conference Held In Oxford In June 2002. In Addition To Articles Arising From The Conference, The Book Also Contains The Famous As Yet Unpublished Article By Graeme Segal On The Definition Of Conformal Field Theories. It Is Ideal As A View Of The Current State Of The Art And Will Appeal To Established Researchers As Well As To Novice Graduate Students. Introduction / Michael Atiyah -- Pt. I. Contributions -- 1. A Variant Of K-theory : K[plus Or Minus] / Michael Atiyah And Michael Hopkins -- 2. Two-vector Bundles And Forms Of Elliptic Cohomology / Nils A. Baas, Bjorn Ian Dundas And John Rognes -- 3. Geometric Realization Of The Segal-sugawara Construction / David Ben-zvi And Edward Frenkel -- 4. Differential Isomorphism And Equivalence Of Algebraic Varieties / Yuri Berest And George Wilson. Edited By Ulrike Tillmann. Includes Bibliographical References. Topological K-theory [2] has many variants which have been developed and exploited for geometric purposes.