Machine generated contents note: Chapter I. Enumerative or reality problems Number of automorphisms of principally polarized abelian varieties -- SANDOR J. KOVACS Rational curves on Grassmannians: Systems theory, reality, and -- transversality -- FRANK SOTTILE Fundamental groups of line arrangements: Enumerative aspects -- ALEXANDER I. SUCIU Chapter II. Variational and moduli problems The formula 12 = 10 + 2 x 1 and its generalizations: Counting rational -- curves on F2 -- DAN ABRAMOVICH AND AARON BERTRAM Stable maps and Hurwitz schemes in mixed characteristics -- DAN ABRAMOVICH AND FRANS OORT On modular properties of odd theta-characteristics -- LUCIA CAPORASO Asymptotic Hodge theory and quantum products -- EDUARDO CATTANI AND JAVIER FERNANDEZ On rational curves in n-space with given normal bundle -- HERBERT CLEMENS A tool for stable reduction of curves on surfaces -- RAVI VAKIL Chapter III. Mirror symmetry and Gromov-Witten invariants Virtual fundamental classes of zero loci -- DAVID A. Cox, SHELDON KATZ, AND YUAN-PIN LEE Gravitational descendants and the moduli space of higher spin curves -- TYLER J. JARVIS, TAKASHI KIMURA, AND ARKADY VAINTROB vii Homological mirror symmetry in dimension one -- BERND KREUf3LER 179 The Hodge structure of semiample hypersurfaces and a generalization of the -- monomial-divisor mirror map -- ANVAR R. MAVLYUTOV 199 Algebraic construction of Witten's top Chern class -- ALEXANDER POLISHCHUK AND ARKADY VAINTROB 229 Symmetries of Gromov-Witten invariants -- ALEXANDER POSTNIKOV 251 Gauge theory techniques in quantum cohomology -- STEVEN ROSENBERG AND MIHAELA VAJIAC 259 Gromov-Witten invariants of flag manifolds and products of conjugacy -- classes -- C. WOODWARD 279 Appendix Appendix: The Lowell meeting 289.