8 problems

Graph-algebra characterization conjecture. The following conditions are equivalent:

Generalized Toms--Winter Conjecture. The following conditions are equivalent:

Toms--Winter Conjecture. The following conditions are equivalent: $$

Divisibility-and-Condition (K) conjecture. The divisibility condition and Condition (K) are equivalent to $$ -stability of the graph algebra.

Let $A$ be a simple, separable, unital, nuclear, $cmathcal{Z}$-stable $C^*$-algebra, let $G$ be a countable, discrete, amenable group, and let…

Let $(X,\alpha)$ be a Kähler manifold with Kähler class $\alpha$. Z-stability conjecture. The manifold $(X,\alpha)$ admits a $Z$-critical Kähler metric in $\alpha$ if and only if…

Equivariant $\mathcal{Z}$-stability conjecture. Equivariant $\mathcal{Z}$-stability is automatic for actions of amenable groups on classifiable $C^*$-algebras.

Let $A$ be a simple separable nuclear $C^*$-algebra. The theorem that $A$ is $\mathcal{Z}$-stable if and only if it has strict comparison is conjectured to continue to hold without…