Willems' conjecture on Brauer character degrees

Let $G$ be a finite group and let $p$ be a prime. Write $|G|_{p'}$ for the prime-to-$p$ part of the order of $G$, and let $\operatorname{IBr}(G)$ denote the irreducible $p$-Brauer characters of $G$. Willems' conjecture.

$$|G|_{p'}\leq\sum_{\varphi\in\operatorname{IBr}(G)}\varphi(1)^2.$$

The conjecture gives a modular analogue of the sum-of-squares formula for ordinary irreducible character degrees. It is known for groups with cyclic Sylow $p$-subgroups, for $p$-solvable groups, and for groups of Lie type in defining characteristic; the paper proves it for all finite groups when $p=2$, while the general case remains open.