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

Thom, René

Publ. Math., Inst. Hautes Étud. Sci. 70, 199-218 (1989).

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

Keywords:

cobordism; singularities of differential maps; catastrophe theory; problems; decompositions of analytic functions; stratifications

References:

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