This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks.This volume contains a selection of expository and research articles by lecturers at the school and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. The book is suitable for graduate students and research mathematicians interested in relations between mathematical physics and algebraic geometry.
The geometry of string theory by M. R. Douglas $M$ theory, $G_2$-manifolds and four dimensional physics by B. S. Acharya Conjectures in Kahler geometry by S. K. Donaldson Branes, calibrations and supergravity by J. P. Gauntlett M-theory on manifolds with exceptional holonomy by S. Gukov Special holonomy and beyond by N. Hitchin Constructing compact manifolds with exceptional holonomy by D. Joyce From Fano threefolds to compact $G_2$-manifolds by A. Kovalev An introduction to motivic integration by A. Craw Representation moduli of the McKay quiver for finite Abelian subgroups of $SL(3,\mathbb{C}$ by A. Ishii Moduli spaces of bundles over Riemann surfaces and the Yang-Mills stratification revisited by F. Kirwan On a classical correspondence between K3 surfaces II by C. Madonna and V. V. Nikulin Contractions and monodromy in homological mirror symmetry by B. Szendroi Lectures on supersymmetric gauge theory by N. Dorey The geometry of A-branes by A. Kapustin Low energy D-brane actions by R. C. Myers List of Participants.
