%0 Journal Article %T A proof of the Faber intersection number conjecture %A Kefeng Liu %A Hao Xu %J Mathematics %D 2008 %I arXiv %X We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of Gromov-Witten invariants. %U http://arxiv.org/abs/0803.2204v3