The Aluffi-Chen-Marcolli Real-Rootedness Conjecture
Aluffi, Chen and Marcolli conjectured that the Poincare polynomial of the Deligne-Mumford moduli space $\overline{\mathcal{M}}_{0,n}$ of stable $n$-pointed rational curves has only real roots. True, with simple roots and strict interlacing between consecutive $n$.