2 problems

Let $n\ge 3$, let $F_n$ be a free group of rank $n$, and let $F$ be a free group. Let $g,h:F_n\to F$ be monomorphisms. Sharp equalizer rank conjecture. Then … The paper constructs…

Infinite equalizer conjecture. There is an upper bound, depending only on $n$, for the number of $\operatorname{Eq}(\phi,\psi)$-orbits of the regular points of…