Jean-Michel Bismut in 2004
(photo from MFO)
26 February 1948 |
|Alma mater||Ecole Polytechnique|
|Doctoral advisor||Jacques-Louis Lions
|Doctoral students||Patrick Cattiaux
|Known for||Probabilistic proof of Atiyah-Singer index theorem|
|Notable awards||Prix Ampère (French Academy of Sciences), 1990|
His early work was related to stochastic differential equations, stochastic control, and Malliavin calculus, to which he made fundamental contributions, giving a probabilistic proof of Hörmander's theorem. He found a heat equation proof for the Atiyah–Singer index theorem. In 1990 he was awarded the Prix Ampere of the Academy of Sciences. He was a visiting scholar at the Institute for Advanced Study in the summer of 1984. He was elected as a member of the French Academy of Sciences in 1991.
- ——— (1973). "Conjugate convex functions in optimal stochastic control". Journal of Mathematical Analysis and Applications 44 (2): 384–404. doi:10.1016/0022-247X(73)90066-8.
- ——— (1981). "Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions". Z. Wahrscheinlichkeitstheorie verw. Gebiete 56 (4): 469–505. doi:10.1007/BF00531428.
- ——— (1986). "The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs". Invent. Math 83: 91–151. doi:10.1007/bf01388755.
- ———; Lebeau, G. (1992). "Complex immersions and Quillen metrics". Inst. Hautes Etudes Scientifiques Pub. Math. 74 (1991).
- ——— (2005). "The hypoelliptic Laplacian on the cotangent bundle". J. Amer. Math. Soc. 18 (2): 379–476.