Around the motivic monodromy conjecture for non-degenerate hypersurfaces

Abstract: 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 $f$, $\exp(2\pi is)$ 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.

algebraic geometry

Audience: researchers in the topic

( paper )

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com