4 problems

Positivity conjecture for motivic Chern classes. For every $u\leq w\in W$,

Kac–Moody extension conjecture. The analogues of the equations giving the Chevalley formulae for $\lambda$ and $-\lambda$ hold for $W$.

New-variable sign conjecture. The coefficients of the $s_i,\delta$-monomials in the $\mathbf{[w]}$-expansion of the $\mC[p]$ classes have sign $(-1)^{\ell(w)}$.

Strict log-concavity conjecture. The coefficients in the $\mathbf{[w]}$-expansion of the non-equivariant $\mC[p]$ classes are strictly log-concave.