6 problems

Let $W_{n,k}^\ast$ be the Kontsevich cycle indexed by nonnegative integers $n$ and $k$, and let $\widetilde{\kappa}_j$ denote the corresponding modified kappa class. Write…

For $g,n\in\mathbb{N}$ with $2g-2+n>0$, let $K_m$ be the homogeneous polynomials in the kappa classes defined by … where … and let…

Top K-polynomial conjecture. One has

Hodge formula conjecture. For $n=0$ or $n=1$, the top polynomial is

Kappa-class vanishing conjecture. The polynomial relations

Proportionality conjecture. For every such $n$, $t$, and $(a_1,\dots,a_n)$, one has