Contemporary Mathematics 2001; 294 pp; softcover Volume: 276 ISBN10: 082182810X ISBN13: 9780821828106 List Price: US$87 Member Price: US$69.60 Order Code: CONM/276
 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, GromovWitten 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 stateoftheart tools, links that connect classical and modern problems, and the latest knowledge available. Readership Graduate students and research mathematicians interested in algebraic geometry and related disciplines. Table of Contents  A. I. Suciu  Fundamental groups of line arrangements: Enumerative aspects
Enumerative or reality problems  S. J. Kovács  Number of automorphisms of principally polarized abelian varieties
 F. Sottile  Rational curves on Grassmannians: Systems theory, reality, and transversality
Variational and moduli problems  D. Abramovich and A. Bertram  The formula \(12 = 10 + 2\times 1\) and its generalizations: Counting rational curves on \(\mathbf{F}_2\)
 D. Abramovich and F. Oort  Stable maps and Hurwitz schemes in mixed characteristics
 L. Caporaso  On modular properties of odd thetacharacteristics
 E. Cattani and J. Fernandez  Asymptotic Hodge theory and quantum products
 H. Clemens  On rational curves in \(n\)space with given normal bundle
 R. Vakil  A tool for stable reduction of curves on surfaces
Mirror symmetry and GromovWitten invariants  D. A. Cox, S. Katz, and Y.P. Lee  Virtual fundamental classes of zero loci
 T. J. Jarvis, T. Kimura, and A. Vaintrob  Gravitational descendants and the moduli space of higher spin curves
 B. Kreußler  Homological mirror symmetry in dimension one
 A. R. Mavlyutov  The Hodge structure of semiample hypersurfaces and a generalization of the monomialdivisor mirror map
 A. Polishchuk and A. Vaintrob  Algebraic construction of Witten's top Chern class
 A. Postnikov  Symmetries of GromovWitten invariants
 S. Rosenberg and M. Vajiac  Gauge theory techniques in quantum cohomology
 C. Woodward  GromovWitten invariants of flag manifolds and products of conjugacy classes
Appendix  E. Previato  The Lowell meeting
