Jarvis, Takashi Kimura and Arkady Vaintrob introduce a new axiom in the theory
of r-spin cohomological field theory and explore its consequences, thus providing
a new geometric meaning for gravitational descendants; Bernd KreuBler provides
results needed in the proof by A. Polishchuk and E. Zaslow of Kontsevich's homo-
logical mirror symmetry for elliptic curves; Anvar Mavlyutov gives a description of
the cohomology of semiample hypersurfaces in a complete simplicial toric variety,
which was previously unknown; Alexander Polishchuk and Arkady Vaintrob give
an algebraic construction for a virtual fundamental class on the moduli space of
curves with higher spin structures; Alexander Postnikov presents new properties
of the Gromov-Witten invariants of complete flag varieties; Steven Rosenberg and
Mihaela Vajiac use gauge theory techniques to give flat sections for the Dubrovin
connection in quantum cohomology; Christopher Woodward's paper is a survey
on related problems such as certain products in conjugacy classes of a Lie group,
Witten's formula for the volumes of moduli spaces of flat connections on Riemann
surfaces, loop groups, and Gromov-Witten invariants of flag manifolds.
Lastly, a word of thanks. Alas, words are inadequate (mine, at least) to portray
the generosity, good cheer and hard work that went into the Lowell enterprise. The
speakers scrambled out of a busy Boston life and into Lowell on DaylightSavingTime
weekend; the writers donated some of their precious summer thinking time; the
referees were startled (in September, first-day-of-classes time!) into reading highly
technical work very quickly, and they did read it closely. And I would also like to
thank warmly Mary Beth Ruskai, who delivered the invited address on Quantum
Information Theory in Lowell and was so good as to suggest my name as a session
organizer. The series Editor, Dr. Dennis DeThrk, was solicitously supportive of this
volume even before
it had much of a shape, and the AMS technical staff responded
with the customary kindness and perfectionism, especially Christine Thivierge. I
hope you enjoy the book!
[BL] A. Beau ville andY. Laszlo, Conformal blocks and generalized theta functions, Comm. Math.
Phys. 164 (1994), 385-419.
[D] J. Dieudonne, History of algebraic geometry, Wadsworth International Group, Belmont, CA,
[H] N.J. Hitchin, Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990),
[M] D. Mumford, An algebra-geometric construction of commuting operators and of solutions
to the Toda lattice equation, Korteweg de Vries equation and related non-linear equations,
Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto,
1977), Kinokuniya Book Store, Tokyo, Japan, 1978, pp. 115-153.
[S] C.L. Siegel, Topics in complex function theory. Vol.
Elliptic functions and uniformization
theory, John Wiley
Sons, Inc., New York, NY, 1988, reprint of the 1969 edition.