# Hodge integrals, partition matrices, and the $\lambda_g$ conjecture

### Abstract

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual localization in Gromov-Witten theory. An analysis of several natural matrices indexed by partitions is required.

## Authors

Carel Faber

Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden

Rahul Pandharipande

Department of Mathematics, Princeton University, Princeton, NJ