Motivic Milnor fibers and Jordan normal forms of monodromies
We introduce a method to calculate the equivariant Hodge-Deligne numbers of toric hypersurfaces. Then we apply it to motivic Milnor fibers introduced by Denef-Loeser and study the Jordan normal forms of the local and global monodromies of polynomial maps in various situations. Especially we focus our attention on monodromies at infinity studied by many people. The results will be explicitly described by the "convexity" of the Newton polyhedra of polynomials. This is a joint work with Y. Matsui and A. Esterov.