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We introduce the theory of local and global monodromies of polynomials incohomology groups in various geometric situations, focusing on its relationswith toric geometry and motivic Milnor fibers, and moreover in the modernlanguages of nearby and vanishing cycle functors. Equivariant mixed Hodgenumbers of motivic Milnor fibers will be described in terms of Newton polyhedraof polynomials.

Geometric monodromies, mixed Hodge numbers of motivic Milnor fibers and Newton polyhedra