Seminar

I will explain some connections between Berkovich spaces of degenerations of Calabi-Yau varieties and the Minimal Model Program in birational geometry. The central object in this theory is the so-called weight function on the Berkovich space. This function has some interesting properties that suggest that one can use it to contract the Berkovich space onto its canonical skeleton. I will also show how analogous properties of weight functions of hypersurface singularities yield a proof of a 1999 conjecture of Veys on poles of maximal order of motivic zeta functions. This is based on joint work with Mircea Mustata and Chenyang Xu.