Objectif My goal is to study several important open mathematical problems in non-equilibrium (NEQ) systems and to build a bridge between these problems and NEQ aspects of soft sciences, in particular biological questions. Traffic on this bridge is going to be two-way, the mathematics carrying a long history as a language of science towards the soft sciences, and the soft sciences fruitfully asking new questions and building new paradigms for mathematical research.Out-of-equilibrium systems pose several fascinating problems: The Fourier law which says that resistance of a wire is proportional to its length is still presenting hard problems for research, and even the existence and the convergence to a NEQ steady state are continuously posing new puzzles, as do questions of smoothness and correlations of such states. These will be addressed with stochastic differential equations, and with particlescatterer systems, both canonical and grand-canonical. The latter are extensions of the well-known Lorentz gas and the study of hyperbolic billiards.Another field where NEQ plays an important role is the study of glassy systems. They were studied with molecular dynamics (MD) but I have used a topological variant, which mimics astonishingly well what happens in MD simulations. The aim is to extend this to 3 dimensions, where new problems appear.Finally, I will apply the NEQ studies to biological systems: How a system copes with the varying environment,adapting in this way to a novel type of NEQ. I will study networks of communication among neurons,which are like random graphs with the additional property of being embedded, and the arrangement of genes on chromosomes in such a way as to optimize the adaptation to the different cell types which must be produced using the same genetic information.I will answer such questions with students and collaborators, who will specialize in the subprojects but will interact with my help across the common bridge. Champ scientifique humanitieshistory and archaeologyhistorynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesbiological sciencesgeneticschromosomes 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) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2011-ADG_20110209 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil UNIVERSITE DE GENEVE Contribution de l’UE € 2 135 385,00 Adresse RUE DU GENERAL DUFOUR 24 1211 Geneve Suisse Voir sur la carte Région Schweiz/Suisse/Svizzera Région lémanique Genève Type d’activité Higher or Secondary Education Establishments Chercheur principal Jean-Pierre Eckmann (Prof.) Contact administratif Alex Waehry (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire UNIVERSITE DE GENEVE Suisse Contribution de l’UE € 2 135 385,00 Adresse RUE DU GENERAL DUFOUR 24 1211 Geneve Voir sur la carte Région Schweiz/Suisse/Svizzera Région lémanique Genève Type d’activité Higher or Secondary Education Establishments Chercheur principal Jean-Pierre Eckmann (Prof.) Contact administratif Alex Waehry (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée