Carlson's depth equality conjecture for finite p-groups

Let $G$ be a finite $p$-group. Define $\omega_a(G)$ as the minimum of $\dim \operatorname{H}^{*}(G;\mathbb{F}_p)/\mathfrak{p}$ over associated primes $\mathfrak{p}$ of $\operatorname{H}^{*}(G;\mathbb{F}_p)$, and let $\omega_d(G)$ be the maximum $s\geq 1$ such that $\operatorname{H}^{*}(G;\mathbb{F}_p)$ is detected by the centralizers of elementary abelian subgroups of rank $s$. Carlson's conjecture. Then

$$\operatorname{depth}\operatorname{H}^{*}(G;\mathbb{F}_p)=\omega_a(G)=\omega_d(G).$$

The preceding inequalities are known, and Carlson conjectured that both are equalities; the supplied text does not state whether the conjecture has been resolved.