Jean-Pierre Ramis

Jean Pierre Ramis (born March 26, 1943 in Montpellier ) is a French mathematician who deals with analysis.

Ramis in Oberwolfach 2008

Ramis grew up in Toulouse , attended the Lycée Louis-le-Grand (where his father Edmond Ramis was Professor of Mathematics and later General Inspector for Education in Mathematics) and the École normal supérieure , where he received his Agrégation in 1965 . He then worked as an assistant at the Faculté des Sciences in Paris. In his Thèse de 3rd cycle he dealt with complex analysis in an infinite number of variables ( Sous-ensembles analytiques d une variete banachique complexe ) and received his doctorate under Henri Cartan (Thèse d'État 1969 with the title Residues et Dualité ). As part of his military service, he taught at the University of Tunis . Then he was at the University of Strasbourg , where he began to deal with differential equations and differential equations in the complex, which became his main field of work. He was temporarily director of the IRMA (Institut de Recherche Mathématique Avancée) in Strasbourg. Since 1994 he has been a professor at the University of Toulouse , where he was head of the mathematics faculty from 2000 to 2005.

In 2005 he became a full member of the Académie des Sciences . In 1982 he received the Prix Doistau-Blutet and in 2002 the Prix Alexandre Joannides of the Académie des Sciences.

He initially dealt with complex analytical geometry in the sense of Cartan and Jean-Pierre Serre . He also expanded the theory of Fuchs' differential equations to include several complex variables. Afterwards he dealt with complex dynamic systems, especially with Galois theory of differential equations such as the proof of an analogue to Abhyankar's conjecture and application to Hamiltonian systems and the question of the complete integrability of these systems (for which he gave a Galois theoretical criterion with Juan Morales , Theory of Ramis-Morales), characterization of the local differential Galois group by Stokes matrices and exponential tori, the wild complex fundamental group , Gevrey series and functions, multi-summation.

Fonts

• with JJ Morales Ruiz: Galoisian obstructions to integrability of Hamiltonian systems, Methods Appl. Anal. 8, Volume 8, 2001, pp. 33-96, 97-112
• with JJ Morales Ruiz, Carles Simó: Integrability of hamiltonian systems and differential Galois groups of higher variational equations, Ann. Sci. Ecole Normale Superieure, 40, 2007, 845-884, numdam

Web links

• Biography, french
• Website at the Academie des Sciences

Individual evidence

1. ↑ Represented in Juan J. Morales Ruiz, Differential Galois theory and non integrability of Hamiltonian systems, Birkhäuser 1999. The Hamiltonian system integrable if and only if the connected component of the one G0 of the differential Galois group G of the associated linear differential equation can be resolved. If G0 is commutative, the Hamiltonian system is integrable. Integrable means representable by integrals, integrals in exponents and algebraic functions.
2. ↑ Martinet, Ramis Elementary acceleration and multisummability , part 1, Annales Inst. Henri Poincaré A, 54, 1991, 331-401 ( Memento of the original from October 4, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked . Please check the original and archive link according to the instructions and then remove this notice.  
3. ↑ Bernard Malgrange , Travaux d ' Ecalle et de Martinet -Ramis sur les systèmes dynamiques, Séminaire Bourbaki 582, 1981/82, Online ( Memento of the original from September 27, 2013 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.