6 problems

Mikhalkin–Zharkov conjecture. The map above is an isomorphism for all $p\geq q$.

Let $X$ be a complex algebraic variety embedded as a tropically compact closed subvariety of a smooth toric variety, and let…

Let $\mathfrak X$ be a smooth projective tropical variety. For an integer $p$, consider the tropical cohomology groups … and let $N$ be the tropical monodromy operator between them…

Cycle-class image conjecture. The image of $\operatorname{CH}(X)_\mathbb{Q}$ is

Liu's conjecture. The iterated monodromy operator above is an isomorphism for all $p\geq q$.

Poincaré duality and ring-structure conjecture. The map $D_F$ is surjective for every tropical variety $F$. If $F$ is regularizable in codimension $1$ and irreducible, then its ker…