Zoghman Mebkhout

Zoghman Mebkhout (* 1949 ) is an Algerian mathematician who deals with algebraic theory of differential equations (theory of D modules). He is the research director of the CNRS .

Zoghman Mebkhout 2006

At the same time as Masaki Kashiwara in 1979 he solved the Riemann-Hilbert problem in higher dimensions ( Riemann-Hilbert correspondence ). He also achieved important results, partly with Gilles Christol, on the structure of the singularities of differential equations in the p-adic case. For example, in 2001 he proved the p-adic monodrome theorem (which relates the behavior of p-adic differential equations near singularities to p-adic Galois representations , similar to the Riemann-Hilbert problem in the complex case). The theorem was conjectured by Richard Crew and proved independently of Yves André and Kiran Kedlaya at about the same time as Mebkhout . The investigations have applications in arithmetic geometry (Galois representations, finiteness theorems for p-adic coefficients). Bernard Dwork and Philippe Robba played a pioneering role in the theory of p-adic differential equations .

Alexander Grothendieck sees Mebkhout with his work in Recoltes et Semaines and L´Enterrement in the late 1970s as a continuation of Grothendieck's own ideas and as wrongly neglected.

In 2002 he received the Prix ​​Servant .

Fonts

• Sur le probleme de Hilbert – Riemann , in Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory (Les Houches Summer School 1979), Lecture notes in physics 129, 1980, pp. 99–110.
• La théorie des equations différentielles p-adiques et le Théorème de la monodromie p-adique , Rev. Mat. Iberoamericana, Volume 19, 2003, pp. 623-665.

Web links

• Conference on his 60th birthday in 2009 in Seville

Individual evidence

1. ↑ z. B. Allyn Jackson Comme Appelé du Néant , Notices AMS, November 2004