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.

Fields of science

• natural sciences › mathematics › applied mathematics › dynamical systems

Programme(s)

• FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Topic(s)

• ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations

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 XI

Address

Rue Georges Clemenceau 15
91405 Orsay
France

Activity type

Higher or Secondary Education Establishments

Administrative Contact

Nicolas Lecompte (Mr.)

Principal investigator

Jean-Michel Philippe Marie-José Bismut (Prof.)

Links

EU contribution

€ 1 112 400

Beneficiaries (1)

UNIVERSITE PARIS-SUD XI

France

EU contribution

€ 1 112 400

Address

Rue Georges Clemenceau 15
91405 Orsay

Activity type

Higher or Secondary Education Establishments

Administrative Contact

Nicolas Lecompte (Mr.)

Principal investigator

Jean-Michel Philippe Marie-José Bismut (Prof.)

Links