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.Let S1 = R/Z, and define a torsion-free G2-structure (alt;p, g) on Sl x y as in Proposition 1.8. ... Calculations by the author indicate that the data needed to do this is a closed, coclosed 1-form a on N that is nonzero at every point of N. The existence ... This may make the method difficult to apply in practice. The second method is studied by Alexei Kovalev , and is based on an idea due to Simon Donaldson.
|Title||:||Strings and Geometry|
|Author||:||Clay Mathematics Institute. Summer School, Isaac Newton Institute for Mathematical Sciences|
|Publisher||:||American Mathematical Soc. - 2004|