CONFRA

"Conformal fractals in analysis, dynamics, physics"

Coordinatore	UNIVERSITE DE GENEVE    more 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

#	participant	country	role	EC contrib. [€]
1	UNIVERSITE DE GENEVE  Organization address address: Rue du General Dufour 24 city: GENEVE postcode: 1211 contact info Titolo: Dr. Nome: Alex Cognome: Waehry Email: send email Telefono: +41 22 379 75 60 Fax: +41 22 379 11 80	CH (GENEVE)	hostInstitution	1˙278˙000.00
2	UNIVERSITE DE GENEVE  Organization address address: Rue du General Dufour 24 city: GENEVE postcode: 1211 contact info Titolo: Prof. Nome: Stanislav Cognome: Smirnov Email: send email Telefono: -3791130 Fax: -3791157	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.'