Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ""Enumerative Geometry in Physics,"" held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.
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978-0-8218-2810-6 (9780821828106)
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Schweitzer Klassifikation
Fundamental groups of line arrangements: Enumerative aspects by A. I. Suciu Enumerative or reality problems: Number of automorphisms of principally polarized abelian varieties by S. J. Kovacs Rational curves on Grassmannians: Systems theory, reality, and transversality by F. Sottile Variational and moduli problems: The formula $12 = 10 + 2\times 1$ and its generalizations: Counting rational curves on $\mathbf{F}_2$ by D. Abramovich and A. Bertram Stable maps and Hurwitz schemes in mixed characteristics by D. Abramovich and F. Oort On modular properties of odd theta-characteristics by L. Caporaso Asymptotic Hodge theory and quantum products by E. Cattani and J. Fernandez On rational curves in $n$-space with given normal bundle by H. Clemens A tool for stable reduction of curves on surfaces by R. Vakil Mirror symmetry and Gromov-Witten invariants: Virtual fundamental classes of zero loci by D. A. Cox, S. Katz, and Y.-P. Lee Gravitational descendants and the moduli space of higher spin curves by T. J. Jarvis, T. Kimura, and A. Vaintrob Homological mirror symmetry in dimension one by B. Kreussler The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map by A. R. Mavlyutov Algebraic construction of Witten's top Chern class by A. Polishchuk and A. Vaintrob Symmetries of Gromov-Witten invariants by A. Postnikov Gauge theory techniques in quantum cohomology by S. Rosenberg and M. Vajiac Gromov-Witten invariants of flag manifolds and products of conjugacy classes by C. Woodward Appendix: The Lowell meeting by E. Previato.
