Objective 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. Fields of science 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) 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 Coordinator UNIVERSITE DE GENEVE Address Rue du general dufour 24 1211 Geneve Switzerland See on map Region Schweiz/Suisse/Svizzera Région lémanique Genève Activity type Higher or Secondary Education Establishments Principal investigator Jean-Pierre Eckmann (Prof.) Administrative Contact Alex Waehry (Dr.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITE DE GENEVE Switzerland EU contribution € 2 135 385,00 Address Rue du general dufour 24 1211 Geneve See on map Region Schweiz/Suisse/Svizzera Région lémanique Genève Activity type Higher or Secondary Education Establishments Principal investigator Jean-Pierre Eckmann (Prof.) Administrative Contact Alex Waehry (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
