Finite Mod_{g,n}-orbits correspond to finite image for large genus

Determine whether, for genus g sufficiently large relative to rank r, a conjugacy class of representations of π1(Σ_{g,n}) has a finite orbit under Mod_{g,n} if and only if its image is finite.

Background

This conjecture posits a clean characterization of finite orbits on character varieties in the high-genus regime. It asserts that finite Mod_{g,n}-orbits should coincide with representations having finite image. The paper later proves this when g≥r^2, giving significant evidence for the conjecture.