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| Name |
Bismut, Jean-Michel |
| Location
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Universite Paris-Saclay |
| Primary Field
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Mathematics |
 Election Citation
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Jean-Michel Bismut studies probability theory, in connection with the Atiyah-Singer index theorem and its local refinements, with applications to eta invariants, analytic torsion, and the trace formula.
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Research Interests
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I have been interested in probability theory, in the Atiyah-Singer index theory and its local refinements, with applications to eta invariants and to real and complex analytic torsion. With Gillet, Lebeau, and Soulé, I participated to the proof of a Riemann-Roch-Grothendieck theorem in Arakelov geometry. With Cheeger, I also worked on adiabatic limits of eta invariants, with Zhang, I gave another proof of the Ray-Singer conjecture on real analytic torsion, and with Lott, I proved an index theorem for flat vector bundles. My more recent work has been devoted to the hypoelliptic Laplacian, a deformation of the classical Laplacian to the generator of the geodesic flow, that Lebeau and myself developed the theory of, with applications to real analytic torsion, to the explicit geometric evaluation of semisimple orbital integrals, and to the proof of a Riemann-Roch-Grothendieck theorem in complex geometry. Probabilistic considerations, various versions of the Dirac operator, as well as Quillen's superconnections have been a constant theme of my work.
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