2 problems

Modulus-of-continuity conjecture. Every group topology on $G$ strictly coarser than $\tau_{st}$ is of the form $\tau_f$ for some $\mathcal{R}$-modulus of continuity.

Hyperimaginary elimination conjecture. The theory $\operatorname{Th}(\mathcal{U}_{\mathcal{R}})$ has elimination of hyperimaginaries if and only if…