Kollár's finiteness conjecture for local fundamental groups of klt singularities

Let $0\in (X,\Delta)$ be a klt singularity. The local fundamental group is

$$\pi^{{\rm loc}}_1(X,0):=\pi_1(L(0\in X)),$$

where $L(0\in X)$ is the link of the singularity. Kollár's finiteness conjecture. The local fundamental group $\pi^{{\rm loc}}_1(X,0)$ is finite.

This conjecture asserts that klt singularities have substantially simpler local topology than log canonical singularities, for which local fundamental groups can be much more complicated. Its resolution status is not established by the supplied text.