¿Jean-Michel Bismut is a French mathematician who is a professor in the Mathematics Department in Orsay. He is known for his contributions to index theory, geometric analysis and probability theory. Together with Gilles Lebeau, he has developed the theory of the hypoelliptic Laplacian, to which he found applications in various fields of mathematics. He shared the Shaw Prize in Mathematical Sciences 2021 with Jeff Cheeger.

Presents a solution to a long-standing problem in complex algebraic geometry

Proves an RRG theorem for coherent sheaves of a compact complex manifold

Offers a valuable resource for many researchers in geometry, analysis, and mathematical physics

Introduction.- Bott-Chern Cohomology and Characteristic Classes.- The Derived Category ${\mathrm{D^{b}_{\mathrm{coh}}}}$.- Preliminaries on Linear Algebra and Differential Geometry.- The Antiholomorphic Superconnections of Block.- An Equivalence of Categories.- Antiholomorphic Superconnections and Generalized Metrics.- Generalized Metrics and Chern Character Forms.- The Case of Embeddings.- Submersions and Elliptic Superconnections.- Elliptic Superconnection Forms and Direct Images.- A Proof of Theorem 10-1 when $\overline{\partial}^{X}\partial^{X}\omega^{X}=0$..- The Hypoelliptic Superconnections.- The Hypoelliptic Superconnection Forms.- The Hypoelliptic Superconnection Forms when $\overline{\partial}^{X}\partial^{X}\omega^{X}=0$.- Exotic Superconnections and Riemann-Roch-Grothendieck.- Subject Index.- Index of Notation.- Bibliography.