Poles of maximal order of motivic zeta functions

We prove a 1999 conjecture of Veys, which says that the opposite of the Log-Canonical threshold is the only possible pole of maximal order of Denef and Loeser's motivic zeta function associated with a germ of a regular function on a smooth variety over a field of characteristic 0. We apply similar methods to study the weight function on the Berkovich skeleton associated with a degeneration of Calabi-Yau varieties. Our results suggest that the weight function induces a flow on the nonarchimedean analytification of the degeneration towards the Kontsevich-Soibelman skeleton.