Objetivo "One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed. This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / Röckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation of nonlinearities (Da Prato / Debussche / etc).Over the past year or so, I have been developing a theory of regularity structures that allows to give a rigorous mathematical interpretation to such equations, which therefore allows to build the mathematical objects conjectured to describe the abovementioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles.If successful, the project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength." Ámbito científico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programa(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) Tema(s) ERC-CG-2013-PE1 - ERC Consolidator Grant - Mathematics Convocatoria de propuestas ERC-2013-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-CG - ERC Consolidator Grants Institución de acogida THE UNIVERSITY OF WARWICK Aportación de la UE € 1 526 234,00 Dirección Kirby Corner Road - University House CV4 8UW Coventry Reino Unido Ver en el mapa Región West Midlands (England) West Midlands Coventry Tipo de actividad Higher or Secondary Education Establishments Investigador principal Martin Hairer (Prof.) Contacto administrativo Catherine Cochrane (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo THE UNIVERSITY OF WARWICK Reino Unido Aportación de la UE € 1 526 234,00 Dirección Kirby Corner Road - University House CV4 8UW Coventry Ver en el mapa Región West Midlands (England) West Midlands Coventry Tipo de actividad Higher or Secondary Education Establishments Investigador principal Martin Hairer (Prof.) Contacto administrativo Catherine Cochrane (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
