Poles of maximal order of motivic zeta functions

I will give a proof of a conjecture of Wim Veys, saying that minus the log canonical threshold of a hypersurface singularity is the only possible pole of maximal order of the motivic zeta function of the singularity. The proof uses recent results from the Minimal Model Program but has a natural interpretation in terms of non-archimedean geometry (weight functions on Berkovich spaces). This is joint work with Chenyang Xu.