Ming Hao Quek (Stanford)

PDL C-38

__Pre-seminar__Title: Introduction to the monodromy conjecture

Abstract: I will give a brief introduction to the monodromy conjecture of Denef—Loeser, which predicts a one-way relationship between two objects arising in singularity theory.

__Seminar__Title: Towards a geometric version of the monodromy conjecture

Abstract: I will formulate a geometric version of the conjecture and elaborate on ongoing work, starting from the case of Newton non-degenerate hypersurfaces. These are hypersurface singularities whose singularities are governed, up to a certain extent, by faces of their Newton polyhedra. The extent to which the former is governed by the latter is a key aspect of the conjecture. Depending on time, I will try to sketch a recent pursuit to reduce the conjecture to a setting that is slightly more general than the case of Newton non-degenerate hypersurfaces.