7 problems

Robert's classification conjecture. The scaled cone of lower-semicontinuous traces classifies separable nuclear $C^*$-algebras up to $a$-tensorisation.

Trace singularity-spectrum conjecture. Theorem $$ holds for every $r\in\mathbb{R}$ simultaneously on a prevalent set.

Let $E$ be a free topological graph, and let ${\mathrm{C}^{*}}(E)$ denote its associated $C^*$-algebra. A tracial state on ${\mathrm{C}^{*}}(E)$ is a positive normalized linear fun…

Let $\Gamma$ be a countable distributive lattice, realized as the lattice of finite ideals of a partially ordered set, and let $A(\Gamma)$ be the $AF$-algebra associated with the H…

Let $G$ be a discrete group, and let … be the Hattori–Stallings trace, where $[G]$ denotes the set of conjugacy classes of elements of $G$. The $C{C}G$ Bass conjecture. The image o…

Codimension conjecture.

None-one-infinity conjecture. The number of traces that an ideal can support must always be either none, one, or infinitely many.