A short proof of the λg-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves.

We give a short and direct proof of Getzler and Pandharipande's λg-conjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the “polynomiality” of Hurwitz numbers, from which we pick off the lowest degree terms. The proof is independent of Gromov-Witten theory. We briefly describe the philosophy behind our general approach to intersection numbers and how it may be extended to other intersection number conjectures. Ideas from this paper feature in two independent recent enlightening proofs of Witten's conjecture by Kazarian [Adv. Math.] and Chen, Li, and Liu [Asian J. Math. 12: 511–518, 2009]. [ABSTRACT FROM AUTHOR]