Ravi Vakil
Published 2006-02-16, updated 2006-02-20Version 2
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and theorems showing that the tautological part of the cohomology ring has a remarkable and profound structure. As an illustration, we describe a new approach to Faber's intersection number conjecture via branched covers of the projective line (work with I.P. Goulden and D.M. Jackson, based on work with T. Graber). En route we review the work of a large number of mathematicians.
Comments: 54 pages, 12 figures; v2 has only small corrections
The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
On an equivalence of divisors on $\bar{M}_{0,n}$ from Gromov-Witten theory and conformal blocks
Gromov-Witten theory and Brane actions I : categorification and K-theory
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