To control the asymptotic of p-adic exponential sums, Igusa proposed the Strong Monodromy Conjecture, which predicts that the p-adic zeta function of an integer coefficient polynomial is governed by the D-module theory over complex numbers. However, there are very few known cases. In this talk, I will explain my recent joint work with Dougal Davis, where we prove this conjecture for any hyperplane arrangement, based on our new theory of multivariate V-filtration and its interaction with the theory of mixed Hodge modules.
