Singularities and Newton Polygons

Abstract

It was conjectured by V. I. Arnold that it should be possible to express all "reasonable" invariants associated to a holomorphic function, in terms of its Newton polygon, at least for "almost all" functions with a given polygon. This conjecture has been worked out in many cases by the joint results of Arnold's school (D. Bernstein, A. Kouchnirenko, A. Varchenko, A. Xovanski). Their results will be the subject of this talk. In particular, the work of Varchenko concerning monodromy and oscillatory integrals should be of great interest in relation with the theory of b-functions.