Ming Hao Quek "Around the motivic monodromy conjecture for non-degenerate hypersurfaces"
Channel: Schubert Seminar
Date: 2022-12-12

Given a complex multivariate polynomial f, the motivic monodromy conjecture states that for every pole s of the motivic zeta function of f, exp(2πis) is a "monodromy eigenvalue" associated to f. I will discuss my (ongoing) work on this conjecture for a "generic" complex multivariate polynomial, namely any polynomial f that is non-degenerate with respect to its Newton polyhedron. 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 which I hope to highlight in my talk, via an example.