Department of Mathematics
Colloquium
by
Prof. Ezra Getzler

The famous WDVV equation gives relations among the Gromov-Witten invariants (enumerative invariants of rational curves) in a compact symplectic manifold. In geometric terms, it corresponds to the definition of a Frobenius manifold. In this talk, we derive some analogous equations for genus 1 and 2 Gromov-Witten invariants, and speculate what their associated geometric structures might be.

References:

1. E. Getzler, Intersection theory on \overline{\scr M}_1,4 and elliptic Gromov-Witten invariants. J. Amer. Math. Soc. 10 (1997), no. 4, 973-998. http://athos.math.nwu.edu/Recent.html alg-geom/9612004

2. W. Fulton, R. Pandharipande Notes on stable maps and quantum cohomology in Algebraic Geometry Santa Cruz 1995, Proceedings of Symposia in Pure Mathematics, 62, eds. J. KollAr, et al alg-geom/9608011