Around the motivic monodromy conjecture for non-degenerate hypersurfaces

I will discuss my ongoing effort to comprehend, from a geometric viewpoint, the motivic monodromy conjecture for a "generic" complex multivariate polynomial f, namely any polynomial f that is non-degenerate with respect to its Newton polyhedron. This conjecture, due to Igusa and Denef--Loeser, states that for every pole s of the motivic zeta function associated to f, exp(2πis) is a "monodromy eigenvalue" associated to f. On the other hand, the non-degeneracy condition on f ensures that the singularity theory of f is governed, up to a certain extent, by faces of the Newton polyhedron of f. The extent to which the former is governed by the latter is one key aspect of the conjecture, and will be the main focus of my talk.

Webpage: https://sites.google.com/view/harvardmitag