Objective Probability is one of the fastest developing areas of mathematics, finding new connections to other branches constantly, from conformal geometry and representation theory to geometric group theory and PDE. It is also indispensable in physics and computer science. A central object is percolation, the simplest example exhibiting phase transition, shedding light on other statistical physics models in two and more dimensions and on Cayley graphs. It is also a key example of how perturbations of the underlying graph influence stochastic processes.Gábor Pete is an expert on most aspects of percolation: conformal invariance, scaling limits, critical exponents, noise sensitivity, renormalization, strongly dependent percolation models, random walks on percolation clusters, and connections to geometric group theory. After almost a decade of successful research in the US and Canada, he would like to return to Europe. The Budapest University of Technology is a well-known center of probability and dynamical systems, with experts on self-interacting random walks, diffusion in disordered media, interacting particle systems, random graphs and fractals.The proposal concerns the following interrelated topics: 1. The advancement of two-dimensional probability by extending the understanding of critical systems to the near-critical regime and proving conformal invariance for new models. 2. Random walks (return probabilities, spectral measures, scaling limits) on groups, quasicrystals, fractal-like graphs. 3. Studying graph limits, dynamically growing graphs, and fractals, via probability and Szemerédi regularity type ideas.The project would introduce conformally invariant and geometric group theoretical probability to Hungary and equip Pete with new tools and points of views. It would establish new collaborative links worldwide, raise the status of the European Research Area, and help reverse brain drain. Fields of science natural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencescomputer and information sciencesnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2010-IIF - Marie Curie Action: "International Incoming Fellowships" Call for proposal FP7-PEOPLE-2010-IIF See other projects for this call Funding Scheme MC-IIF - International Incoming Fellowships (IIF) Coordinator BUDAPESTI MUSZAKI ES GAZDASAGTUDOMANYI EGYETEM Address Muegyetem rakpart 3 1111 Budapest Hungary See on map Region Közép-Magyarország Budapest Budapest Activity type Higher or Secondary Education Establishments Administrative Contact Bálint Tóth (Prof.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data
