researchseminars.org

Matt Larson (Stanford)
2022-10-21 19:00 - 20:00 UTC | https://researchseminars.org/talk/agstanford/99/
Title: The local motivic monodromy conjecture for simplicial nondegenerate singularities (https://researchseminars.org/talk/agstanford/99/)
by Matt Larson (Stanford) as part of Stanford algebraic geometry seminar

Lecture held in 383-N.

Abstract
The monodromy conjecture predicts a relationship between the motivic zeta function of a hypersurface V(f), which governs the number of solutions to f = 0 (mod p^n) if f has integer coefficients and p is a sufficiently large prime, and the eigenvalues of the monodromy action on the cohomology of the Milnor fiber, which is a topological invariant of the complex hypersurface. When f is nondegenerate with respect to its Newton polyhedron, which is true for "generic" polynomials, there are combinatorial formulas for both the motivic zeta function and the eigenvalue of monodromy. I will describe recent results (joint with S. Payne and A. Stapledon) which prove a version of the monodromy conjecture for nondegenerate polynomials which have a simplicial Newton polyhedron.
