Paul Georges Malliavin

His career is devoted to Mathematical Analysis understood in a comprehensive sense. He helped solve the conjecture raised by Norbert Wiener in 1932, the Spectral Synthesis in Fourier Analysis. Another conjecture, raised by Paley-Wiener, and studied extensively by Norman Levinson, the calculus of Radius of Totality of a sequence complex exponentials was solved in collaboration with Arne Beurling. The work goes over on several complex variables; there the Lusin Area integral theory, classical in one complex variable, was fitted in the polydisk of n variables. The works in one or several complex variables uses extensively methods of potential theory. The need for effective estimates in potential theory leads in the seventies to a new start in Probability Theory. The approach put in this framework was worked out on the influence of Geometry and also Functional Analysis: it is generally known as Malliavin Calculus In particular it makes possible to prove a conjecture on the formula of integration by part of Wiener measure on Loop Groups; in the hands of others Mathematicians it lead to new results in either in Statistical Mechanics or in Financial Mechanics. His current works are related to Geometry in infinite dimension within its relations to Stochastic Analysis.