Geometry and Physics

Contents -- Preface -- Contributors -- Opening Address -- Geometry and physics: where are we going? /Sir Michael Atiyah -- Summer School Notes -- Floer homology, A?-categories and topological field theory /Kenji Fukaya, notes by Paul Seidel -- Quantum field theory, equivariant cohomology, symplectic geometry and moduli spaces of vector bundles on Riemann surfaces /Lisa C. Jeffrey -- Notes on Seiberg-Witten invariants /Zoltdn Szabo -- An introduction to the topology of the moduli space of stable bundles on a Riemann surface /Michael Thaddeus -- The fundamental theorem of Vassiliev invariants /Dror Bar-Natan, notes by Alexander Stoimenow -- Conference and Workshop Papers -- Configuration spaces and imbedding problems /Raoul Bott -- Topology of the space of SU(2)-monopoles in M3 /Graeme Segal -- Recent progress on Kahler-Einstein metrics /Gang Tian -- The ODE system arising from cohomogeneity one Einstein metrics /J.-H. Eschenburg and McKenzie Y. Wang -- Einstein metrics on complex surfaces /Claude LeBrun -- BPS states as symplectic invariants from string theory /Shing-Tung Yau and Eric Zaslow -- Determinant line bundles revisited /Daniel S. Freed -- On representations of spin mapping class groups arising in Spin TQFT /G. Masbaum -- The symplectic S-cobordism conjecture: a summary /Kenji Fukaya -- Hamiltonian torus actions /Yael Karshon -- A new proof of the convexity theorem for the Poisson-Lie moment map /A. Yu. Alekseev -- Symplectic 4-manifolds with = 1 /Hiroshi Ohta and Kaoru Ono -- Compact manifolds with exceptional holonomy /Dominic Joyce -- Fusion product of positive level representations and Lie algebra homology /Shrawan Kumar -- Affine connections on involutive G'-structures /Sergey A. Merkulov -- Observations on the topology of symmetric spaces /A. Fino and S. Salamon -- Hyperkahler metrics on cotangent bundles of Hermitian symmetric spaces /Olivier Biquard and Paul Gauduchon -- Decomposable self-dual manifolds /Y. S. Boon -- The SJ7(oo)-Toda field equation and special four-dimensional metrics /K. P. Tod -- The structure of quaternionic Kahler quotients /Andrew Dancer and Andrew Swann -- Overview and warmup example for perturbation theory with instantons /Scott Axelrod -- A note on free composition of subfactors /Dietmar Bisch and Vaughan Jones -- Witten-Reshetikhin-Turaev invariants of 3-manifolds as holomorphic functions /R. J. Lawrence -- On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten-Reshetikhin-Turaev invariant /L. Rozansky -- A quantum s /2-invariant of 3-manifolds which contains all the Witten-Reshetikhin-Turaev invariants /Thang T. Q. Le -- On some invariants of 3-manifolds /Tomotada Ohtsuki -- Quantum Sp(2) invariants of three-manifolds at eighth and tenth roots of unity /Hitoshi Murakami and Tomotada Ohtsuki -- On finite type 3-manifold invariants V: rational homology 3-spheres /Stavros Garoufalidis and Tomotada Ohtsuki -- The Casson invariant for a knot in a 3-manifold /Jun Murakami -- Invariants of links and three-manifolds via Hopf algebras /Louis H. Kauffman -- Portrait of the handle as a Hopf algebra /David Yetter -- Genealogy of non-perturbative quantum-invariants of 3-manifolds: the surgical family /Thomas Kerler -- Finite order invariants of framed knots in a solid torus and in Arnold's J+-theory of plane curves /V. Goryunov -- Numerical application of quantum invariants to random knotting /Tetsuo Deguchi and Kyoichi Tsurusaki -- Non-Abelian monopoles and vortices /Steven B. Bradlow and Oscar Garcia-Prada -- Seiberg-Witten and Gromov invariants /Clifford H. Taubes -- Introduction to conformal field theory with gauge symmetries /Kenji Ueno.