Contents Preface vii Scientific Program ix Part 1 Spaces of stability conditions T. Bridgeland 1 The crepant resolution conjecture J. Bryan and T. Graber 23 Surfaces in background space and the homology of mapping class groups R. L. 43 Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus I. Coskun and R. Vakil 77 The global geometry of the moduli space of curves G. Farkas 125 The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations M. Gross 149 Geometry of S. Grushevsky 193 The global Torelli theorem: classical, derived, twisted D. Huybrechts 235 On the geometry of Deligne-Mumford stacks A. Kresch 259 Moduli spaces of sheaves and principal G-bundles A. Langer 273 Notes on axiomatic Gromov-Witten theory and applications Y.-P. Lee 309 Gromov-Witten theory, Hurwitz numbers, and matrix models A. Okounkov and R. Pandharipande 325 Symplectic homology as Hochschild homology P. Seidel 415 v Ag and its compactifications Cohen and I. Madsen

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