Zoghman Mebkhout
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Zoghman Mebkhout (born 1949) (مبخوت زغمان) is an Algerian mathematician known for his work in algebraic analysis, geometry, and representation theory, more precisely on the theory of D-modules . | image File:Http://owpdb.mfo.de/photoNormal?id=8510
Zoghman is one of the first international-caliber North-African mathematicians, having had his symposium in Spain for his 60'th birthday.
However, as Grothendieck says in 'Récoltes et Sémailles' [1], his high-quality work has been long neglected by French mathematicians such as Pierre Deligne and some other ex-students of Grothendieck, and surprisingly not by their master, mainly because of Zoghman's ethnical origins, as some French mathematicians still neglect the work of brilliant North-African minds. Zoghman is an example of this hidden phenomena in the French School of Mathematics.
Alexander Grothendieck says in page 106 of "Récoltes et Sémailles ": La "version Mebkhout" dont j’ai voulu me faire l’interprète, me semble consister pour l’essentiel en les deux thèses que voici :1. Entre 1972 et 1979, Mebkhout aurait été seul, dans l’indifférence générale et en s’inspirant de mon oeuvre, à développer la "philosophie des D -Modules ", en tant que nouvelle théorie des "coefficients cohomologiques" en mon sens.2. Il y aurait eu un consensus unanime, tant en France qu’au niveau international, pour escamoter son nom et son rôle dans cette théorie nouvelle, une fois que sa portée a commencé à être reconnue.
Grothendieck says that Mebkhout's name was hidden and his role neglected for a theory he was the first to develop.
Notable works : Zoghman Mebkhout proved the Riemann–Hilbert correspondence[2], which is a generalization of Hilbert's twenty-first problem to higher dimensions. The original setting was for Riemann surfaces, where it was about the existence of regular differential equations with prescribed monodromy groups. In higher dimensions, Riemann surfaces are replaced by complex manifolds of dimension > 1, and there is a correspondence between certain systems of partial differential equations (linear and having very special properties for their solutions) and possible monodromies of their solutions.
The result was also proved independently by Masaki Kashiwara[3]. Zoghman is largely known as a specialist of D-modules theory [1].
References
- ^ a b Alexander Grothendieck, "Récoltes et sémailles, Réflexions et témoignage sur un passé de mathématicien."
- ^ Z. Mebkhout, Sur le probleme de Hilbert–Riemann, Lecture notes in physics 129 (1980) 99–110.
- ^ M. Kashiwara, Faisceaux constructibles et systemes holonomes d'équations aux derivées partielles linéaires à points singuliers réguliers, Se. Goulaouic-Schwartz, 1979–80, Exp. 19.
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