Academic DegreesDoctorat de 3. Cycle: Université de Nice-Sofia Antipolis, 1978. Supervisor: J. Chazarain (Nice). Title of thesis: "Hypoellipticité partielle à la frontière des opérateurs pseudo-différentiels de transmission".
My supervisor was Jacques Chazarain, at that time a leading specialist in partial differential equations (he now works in artificial intelligence). The subject of my thesis was a microlocal study of the transmission property for pseudo-differential opeartors, with applications to partial hypoellipticity. I later extended this work in a series of articles; in particular I succeded in defining a notion of "boundary wavefront set", which behaved well under the action of pseudo-differential operators with the transmission property
Habilitation à Diriger des Recherches: Université Pierre et Marie Curie (Paris 6), 1992. My mentor was Jean Leray (Collège de France), one of the great mathematicians of last century. Did you know that Leray invented sheaf theory and spectral sequences while being a prisoner of war in Austria during WWII? See Haynes Miller's text in Gaz. Math. No. 84 (2000), 17-34 "Leray in Oflag XVIIA http://www.freewebs.com/cvdegosson/LerayOflag.ps. The "Habilitation" is a very high-level French diploma which is necessary for applying for a professorship in France; it replaces the former Doctorat d'État. I was Leray's last student; his mentorship was actually unofficial since he was at that time over 85 years old: the French motto was (and still is!) place aux jeunes! My Habilitation thesis consisted of a series of papers, on partial differential equations and on a topological and combinatorial study of the Maslov index, with applications to the theory of the metaplectic group.