This paper contains a survey of research on critical points of smooth functions and their
bifurcations. We indicate applications to the theory of Lagrangian singularities (caustics) …

An analysis of the normal forms to which functions can be reduced in neighbourhoods of
degenerate critical points shows that many of them are quasihomogeneous or …

En mémoire de GN Tiurina li des résultats principaux de cet article est la démonstration
d'une formule liant le nombre de Milnor (d'un point singulier isolé d'un germe d'une fonction …

Intégrales asymptotiques et monodromie Page 1 ANNALES SCIENTIFIQUES DE L’É.NS
BERNARD MALGRANGE Intégrales asymptotiques et monodromie Annales scientifiques …

Given an open set of C or, more generally, a Riemann surface X, a discrete subset Y of X
and a differential form co= j {z) dz, in a local coordinate z, which is holomorphic in X\Y …

Given a polynomial function with an isolated zero at the origin, we prove that the local A 1-
Brouwer degree equals the Eisenbud–Khimshiashvili–Levine class. This answers a …

This is a survey of the main directions in the theory of deformations of complex spaces. It
touches on related questions: deformations of maps, cohomology of algebras, topology of …

We study integrals of rapidly oscillating functions. Such integrals tend to zero when the
length of the oscillation wave tends to zero through wave fronts of constant form. The …

The theory of complex analytic sets is part of the modern geometric theory of functions of
several complex variables. Traditionally, the presentation of the foundations of the theory of …

N= 2 supersymmetry in two dimensions can be seen as a quantum realization of the
geometry of singularity theory. We show this using non-perturbative methods. N= 2 susy is …