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The analysis of the Dirac operator: the hypoelliptic Laplacian and its applications

Objective

This proposal is devoted to the applications of a new hypoelliptic Dirac operator,
whose analytic properties have been studied by Lebeau and myself. Its construction connects classical Hodge theory with the geodesic flow, and more generally any geometrically defined Hodge Laplacian with a dynamical system on the cotangent bundle. The proper description of this object can be given in analytic, index theoretic and probabilistic terms, which explains both its potential many applications, and also its complexity.

Field of science

  • /natural sciences/mathematics/applied mathematics/dynamical systems

Call for proposal

ERC-2011-ADG_20110209
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

UNIVERSITE PARIS-SUD
Address
Rue Georges Clemenceau 15
91405 Orsay Cedex
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 112 400
Principal investigator
Jean-Michel Philippe Marie-José Bismut (Prof.)
Administrative Contact
Nicolas Lecompte (Mr.)

Beneficiaries (1)

UNIVERSITE PARIS-SUD
France
EU contribution
€ 1 112 400
Address
Rue Georges Clemenceau 15
91405 Orsay Cedex
Activity type
Higher or Secondary Education Establishments
Principal investigator
Jean-Michel Philippe Marie-José Bismut (Prof.)
Administrative Contact
Nicolas Lecompte (Mr.)