CONFRA
"Conformal fractals in analysis, dynamics, physics"
| Coordinatore | UNIVERSITE DE GENEVE
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Switzerland [CH] |
| Totale costo | 1˙278˙000 € |
| EC contributo | 1˙278˙000 € |
| Programma | 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) |
| Code Call | ERC-2008-AdG |
| Funding Scheme | ERC-AG |
| Anno di inizio | 2009 |
| Periodo (anno-mese-giorno) | 2009-01-01 - 2013-12-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITE DE GENEVE
Organization address
address: Rue du General Dufour 24 contact info |
CH (GENEVE) | hostInstitution | 1˙278˙000.00 |
| 2 |
UNIVERSITE DE GENEVE
Organization address
address: Rue du General Dufour 24 contact info |
CH (GENEVE) | hostInstitution | 1˙278˙000.00 |
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Obiettivo del progetto (Objective)
'The goal of this project is to study conformally invariant fractal structures from the perspectives of analysis, dynamics, probability, geometry and physics, emphasizing interrelations of these fields. In the last two decades such structures emerged in several areas: continuum scaling limits of 2D critical models in statistical physics (percolation, Ising model); extremal configurations for various problems in complex analysis (multifractal harmonic measures, coefficient growth of univalent maps, Brennan's conjecture); chaotic sets for complex dynamical systems (Julia sets, Kleinian groups). Capitalizing on recent successes, I plan to continue my work in these areas, exploiting their interactions and connections to physics. I intend to achieve at least some of the following goals: * To establish that several critical lattice models have conformally invariant scaling limits, by building upon results on percolation and Ising models and finding discrete holomorphic observables. * To study geometric properties of arising fractal curves and random fields by connecting them to Schramm's SLE curves and Gaussian Free Fields. * To investigate massive scaling limits by describing them geometrically with generalizations of SLEs. * To lay mathematical framework behind relevant physical notions, such as Coulomb Gas (by relating height functions to GFFs) and Quantum Gravity (by identifying limits of random planar graphs with Liouville QGs). * To improve known bounds in several old questions in complex analysis by studying multifractal spectra of harmonic measures. * To estimate extremal behavior of such spectra by using holomorphic motions of (quasi) conformal maps and thermodynamic formalism. * To understand nature of extremal multifractals for harmonic measure by studying random and dynamical fractals. The topics involved range from century old to very young ones. Recently connections between them started to emerge, opening exciting possibilities for new developments in some long standing open problems.'