Zoghman Mebkhout

Zoghman Mebkhout (born 1949 ) (مبخوت زغمان) is a French-Algerian mathematician known for his work in algebraic analysis, geometry, and representation theory, more precisely on the theory of D-modules.

Zoghman is one of the first modern international-caliber North-African mathematicians, a symposium in Spain having been held on his sixtieth birthday, he was also invited to the Institute for Advanced Study on two occasions.

Alexander Grothendieck writes on page 106 of "Récoltes et Sémailles":

Grothendieck says that Mebkhout's name was hidden and his role neglected for a theory Zoghman was the first to develop.

Zoghman Mebkhout is currently a research director at the French National Centre for Scientific Research.In 2002 Zoghman received the Servant Medal from the CNRS.

Zoghman Mebkhout proved in September 1979 the Riemann–Hilbert correspondence, 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. See http://adsabs.harvard.edu/abs/1980LNP...126...90M The result was also proved independently by Masaki Kashiwara 8 months later in April 1980. See "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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