Gromov-Witten Theory and the Geometry of the Moduli Space of Curves

California Institute Of Technology, Pasadena CA

Investigators

Abstract

Pandharipande will study problems in the Gromov-Witten theory of algebraic varieties. In the first two parts, recently developed methods in Gromov-Witten theory will be used to study the geometry of the moduli space of curves. In particular, Hodge integrals and tautological rings will be studied. The third part of the project is an investigation of the Toda equation for the potential of the projective line. The fourth part is a study of degenerate and multiple cover calculations for threefolds and their relationship to M-theory. In this project, Pandharipande will study basic questions in the geometry of Riemann surfaces using new ideas from topological string theory. The research undertaken will involve computations of basic integral series that play a central role in Gromov-Witten theory. Also, the current perspective leads to many fundamental new lines of inquiry that will be pursued. The whole subject lies on the boundary of several fields of mathematics and string theory.