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