Zoghman Mebkhout (مبخوت زغمان) is an Algeria

Algeria

Algeria , officially the People's Democratic Republic of Algeria , also formally referred to as the Democratic and Popular Republic of Algeria, is a country in the Maghreb region of Northwest Africa with Algiers as its capital.In terms of land area, it is the largest country in Africa and the Arab...

n mathematician known for his work in algebraic analysis

Algebraic analysis

Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions.-See also:...

, geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, and representation theory

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...

, more precisely on the theory of D-module

D-module

In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations...

s .

Zoghman is one of the first international caliber north african mathematician ,having had his symposium in Spain for his 60'th
birthday .

However as Grothendieck says in 'récoltes et sémailles' his high quality work has been long neglected by french mathematicians such as Pierre Deligne and some other ex-students of Grothendieck mainly because of personal differences.
Zoghman Mebkhout proved the Riemann–Hilbert correspondence

Riemann–Hilbert correspondence

In mathematics, the Riemann–Hilbert correspondence 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...

, which is a generalization of Hilbert's twenty-first problem

Hilbert's twenty-first problem

The twenty-first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, was phrased like this ....

 to higher dimensions. The original setting was for Riemann surface

Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as "deformed versions" of the complex plane: locally near every point they look like patches of the...

s, where it was about the existence of regular differential equations with prescribed monodromy groups. In higher dimensions, Riemann surfaces are replaced by complex manifold

Complex manifold

In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic....

s of dimension > 1, and there is a correspondence between certain systems of partial differential equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s (linear and having very special properties for their solutions) and possible monodromies of their solutions.

The result was secondly proved after independently by Masaki Kashiwara

Masaki Kashiwara

is a Japanese mathematician. He was a student of Mikio Sato at the University of Tokyo. Sato and Kashiwara have collaborated on algebraic analysis and D-module theory.He is a member of the French Academy of Sciences.- Concepts named after Kashiwara :...

.