2 problems

Flag local $h$-polynomial $\gamma$-positivity conjecture. The local $h$-polynomial $\ell_V(\Gamma,x)$ is $\gamma$-positive whenever $\Gamma$ is flag.

Stanley's conjectures. The polynomial $\ell_V(\Gamma,x)$ has unimodal coefficients for every simplicial subdivision $\Gamma$ of $2^V$, and, for every flag simplicial subdivision, t…