5 problems

Let $A$ be a simple separable unital nuclear $C^*$-algebra. The Toms–Winter conjecture. Finite nuclear dimension of $A$, tensorial absorption of the Jiang–Su algebra $\mathcal{Z}$,…

Finite Hirsch length conjecture. The group $G$ has finite Hirsch length if and only if

Relative complexity conjecture. Every separable $C^*$-algebra with finite nuclear dimension has finite complexity relative to the class of subhomogeneous $C^*$-algebras.

Finite-complexity conjecture. Every separable $C^*$-algebra with finite nuclear dimension and real rank zero has finite complexity.

Let $A$ be a separable, simple, unital, infinite-dimensional, nuclear $C^*$-algebra. The Toms' regularity conjecture. The following conditions are equivalent: 1. $A$ has finite nuc…