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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.

Call for proposal

ERC-2011-ADG_20110209
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Host institution

UNIVERSITE PARIS-SUD XI
Address
Rue Georges Clemenceau 15
91405 Orsay
France

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Activity type
Higher or Secondary Education Establishments
Administrative Contact
Nicolas Lecompte (Mr.)
Principal investigator
Jean-Michel Philippe Marie-José Bismut (Prof.)
EU contribution
€ 1 112 400

Beneficiaries (1)

UNIVERSITE PARIS-SUD XI
France
EU contribution
€ 1 112 400
Address
Rue Georges Clemenceau 15
91405 Orsay

See on map

Activity type
Higher or Secondary Education Establishments
Administrative Contact
Nicolas Lecompte (Mr.)
Principal investigator
Jean-Michel Philippe Marie-José Bismut (Prof.)