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Problèmes rencontrés dans mon parcours mathématique: Un bilan. (Problems I have come across during my mathematical career: A balance). (French) Zbl 0709.58001

The paper is based on the address delivered by the author at the symposium in his honor held in Paris in 1988.
At first the author sketches his personal history and describes the main steps of his research activity: cobordism, singularities of differential maps, catastrophe theory. Then he points out some problems he has studied during his life and outlines some research programs starting from them. The subjects are too technical and have too many mutual implications to be summarized in the narrow space of a review. The paper itself indeed is a review of the problems the author has come across during his exceptional mathematical career. The main topics the problems concern are: decompositions of analytic functions, canonical stratifications of function spaces, algebraic actions of non-compact groups, non-separated stratified spaces.
Reviewer: A.Tancredi

MSC:

58-02 Research exposition (monographs, survey articles) pertaining to global analysis
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
01A70 Biographies, obituaries, personalia, bibliographies
32A10 Holomorphic functions of several complex variables
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
01A65 Development of contemporary mathematics
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References:

[1] J.-P. Françoise, Systèmes maximaux d’une singularité quasi homogène,C.R.A.S., série A,290 (16 juin 1980), 1061–1064.
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[3] E. Heil, Concurrent normals and critical points under weak smoothness assumptions, inDiscrete Geometry and Convexity, ed. J. E. Goodman,Ann. New York Acad. Sci.,440 (1985), 170–178. Cet article mentionne les conjectures de Hentschke et Zamfirescu rapportées dans le texte.
[4] J.-P. Dufour, Sur la stabilité des diagrammes d’applications différentiables,Ann. Sci. Ecole Normale Sup. (4),10 (1977), 153–174.
[5] S. Smale (avecM. Shub), Computational complexity. On the geometry of polynomials and a theory of cost,Ann. Sci. Ecole Normale Sup.,18 (1985), 107–142. · Zbl 0603.65027
[6] Shih Wei Shu, Une méthode élémentaire pour l’étude des équations aux dérivées partielles,Diagrammes, vol. 16, Paris, Université de Paris VII, 1986.
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