SubsidieMeestersStochastic PDEs and Renormalisation
This project aims to advance the study of singular SPDEs by exploring Gibbs measures, developing quasilinear renormalisation, and improving approximation methods for enhanced convergence.
Projectdetails
Introduction
The field of stochastic partial differential equations (SPDEs) has been revolutionised in the last decade by breakthrough works of Hairer, Gubinelli-Imkeller-Perkowski, and many others. A new understanding of renormalised solution theories emerged, solving long-standing singular equations arising in various areas of probability and mathematical physics.
Project Purpose
The purpose of this project is to study a number of important questions in the field, open new directions, and challenge central open problems:
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Launch the investigation of singular SPDEs that preserve Gibbs measures of distributional Hamiltonians such as the density of self-repellent polymers.
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Tackle the question of a quasilinear renormalisation formula, the last remaining component of the quasilinear solution theory.
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Develop an efficient quantitative approximation theory of singular SPDEs, removing the criticality barrier from the rate of convergence.
Financiële details & Tijdlijn
Financiële details
| Subsidiebedrag | € 1.498.849 |
| Totale projectbegroting | € 1.498.849 |
Tijdlijn
| Startdatum | 1-3-2024 |
| Einddatum | 28-2-2029 |
| Subsidiejaar | 2024 |
Partners & Locaties
Projectpartners
- TECHNISCHE UNIVERSITAET WIENpenvoerder
Land(en)
Vergelijkbare projecten binnen European Research Council
| Project | Regeling | Bedrag | Jaar | Actie |
|---|---|---|---|---|
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Global Estimates for non-linear stochastic PDEs
This project aims to analyze the global behavior of solutions to non-linear stochastic partial differential equations, enhancing understanding of mathematical physics models through advanced PDE techniques.
Fluctuations in continuum and conservative stochastic partial differential equations
The project aims to analyze conservative stochastic partial differential equations to uncover universal properties and advance mathematical methods in complex dynamical systems influenced by fluctuations.
Low Regularity Dynamics via Decorated Trees
This project aims to enhance the resolution of singular SPDEs and dispersive PDEs using decorated trees and Hopf algebraic structures, integrating algebraic tools across various fields.
Beyond Renormalization in Parabolic Dynamics
This project aims to advance the ergodic theory of parabolic dynamical systems by developing a unified approach to effective ergodicity and addressing key open questions in various examples.
Stable solutions and nonstandard diffusions: PDE questions arising in Mathematical Physics
This project aims to explore the mathematics of diffusion through the classification of stable solutions to reaction-diffusion PDEs and the study of nonstandard diffusion models.