Wim Veys : Zeta functions and monodromy

Posted by , part of the Algebraic Geometry Seminar.

At

April 15, 2008, 3 p.m.

In

SEO 512

Abstract

To a p-adic or complex polynomial f one associates its p-adic Igusa zeta function, motivic or topological zeta function. There is an intriguing 'monodromy conjecture', predicting that poles of these zeta functions induce eigenvalues of the local monodromy of f. Up to now the conjecture is proven only for polynomials in two variables. We want to report on quite general results for polynomials f in three variables, and mention the link with certain configurations of plane curves and with principal value integrals.