# Seminar of Algebra

### Motivic Milnor fibers and their virtual Betti numbers

Speaker:
Kiyoshi Takeuchi (University of Tsukuba)
Email:
takechan@math.tsukuba.ac.jp
Location:
Departamento de Álgebra
Date:
Fri, 27 jun 2014 16:00
Bio:
Kiyoshi Takeuchi es profesor en la Facultad de Ciencias Puras y Aplicadas de la Universidad de Tsukuba. Sus áreas de investigación son $\mathcal{D}$-módulos, análisis microlocal, haces perversos y funciones hipergeométricas.

By computing the equivariant mixed Hodge numbers of motivic Milnor fibers introduced by Denef-Loeser etc., we obtain various formulae for the Jordan normal forms of the local and global monodromies of polynomials. Especially we focus our attention on the global ones, i.e., the monodromies at infinity. For polynomials over affine complete intersection varieties the results will be described by the mixed volumes of the faces of their Newton polyhedra.

This is a joint work with Y. Matsui and A. Esterov.