Plenary Lecture

Applications of the Malliavin Calculus of Bismut type without probability

Professor Remi Leandre
Institut de Mathematiques. Universite de Bourgogne
21000. Dijon. FRANCE
Remi.leandre@u-bourgogne.fr

Abstract: The talk is divided in 5 parts:

• In the first part, we translate Malliavin Calculus of Bismut type in
  semi-group theory.

• In the second part, we translate in semi-group theory Varadhan estimates
  we have got a long time ago by using the Malliavin Calculus.

• In the third part, we translate in semi-group theory the positivity
  theorem we got Ben Arous and us by using the Bismutian procedure.

• In the fourth part, we translate in semi-group theory some results we got
  a lot of time ago by using the translation in probability of the
  Rothschild-Stein division method.

• In the fifth part, we translate in semi group theory the Girsanov formula
  for jump processe, which is at the basis of Bismut's approach of the
  Malliavin Calculus for Poisson processes.

Brief Biography of the Speaker:
1957: Born in Belfort (France).
1978/1981: Student Ecole Normale Superieure Saint-Cloud.
1980: Agregation de Mathematiques. Rank: 5.
1982/1984: National service at the University of Monastir (Tunisia).
1984: These de Troisieme cycle. Directeur: J.M. Bismut.
1984/1988: assistant at the Universite de Besancon.
1987: Habilitation a diriger les recherches. Universite de Besancon. Directeur: J.M. Bismut.
1988: Bronze medal of C.N.R.S.
1988/1994: Charge de recherches Premiere classe C.N.R.S. Universite de Strasbourg.
1989: Rollo Davidson Price.
1994/2004: Directeur de recherches Seconde Classe. C.N.R.S. Universite de Nancy.
2003: Editor of a special issue ”Probability and geometry” of the Journal ”Infinite dimensional analysis, quantum probability and related topics”.
2004: Directeur de recherches Seconde Classe. Universite de Dijon.

Professor Leandre has organised various conferences.