Interacting fronts in the strongly nonlocal Allen--Cahn equation

We study the sharp-interface limit of the fractional Allen--Cahn equation in $\R^n$, $n\geq 2$, in the strongly nonlocal regime $s\in(0,\frac12)$, for initial data consisting of finitely many nested transition layers. We identify a coupled geometric law for the motion of the resulting fronts: each v