Geometry and Physics

Opening address: geometry and physics - where we going? Summer School notes: Floer homology, A-infinity categories and topological field theory; quantum field theory, equivalent cohomology, symplectic geometry, and moduli spaces of vector bundles on Riemann surfaces; notes on Seiberg-Witten invariants; an introduction to the topology of the moduli space of stable bundles on a Riemann surface; the fundamental theorem of Vassiliev invariants. Conference and workshop papers: configuration spaces and imbedding problems; topology of the space of SU(2)-monopoles in R3; recent progress on Kahler-Einstein metrics; the ODE system arising from cohomogeneity One Einstein metrics; Einstein metrics on complex surfaces; BPS states as symplectic invariants from string theory; determinants line bundles revisited; on representations of spin mapping class groups arising in spin TQFT; the symplectic S-Cobodism conjecture - a summary; Hamiltonian Torus action; a new proof of the convexity theorem for the poisson-lie moment map; symplectic 4-manifolds with b2+=1; compact manifolds with exceptional holonomy; fusion product of positive level representations and lie algebra homology; affine connections on involutive G-structures; observations on the topology of symmetric spaces; hyperkahler metrics on cotangent bundles of Hermitian symmetric spaces; decomposable self-dual manifolds; the SU infinity - Toda filed equation and special four-dimensional metrics; the structure of quaternionic Kahler quotients; overview and warmup example for perturbation theory with instantons; a note on free composition of subfactors. (Part contents).