Summary
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. The purpose of this project is to study a number of important questions in the field, open new directions, and challenge central open problems:
(i) Launch the investigation of singular SPDEs that preserve Gibbs measures of distributional Hamiltonians such as the density of self-repellent polymers;
(ii) Tackle the question of a quasilinear renormalisation formula, the last remaining component of the quasilinear solution theory;
(iii) Develop an efficient quantitative approximation theory of singular SPDEs, removing the criticality barrier from the rate of convergence.
(i) Launch the investigation of singular SPDEs that preserve Gibbs measures of distributional Hamiltonians such as the density of self-repellent polymers;
(ii) Tackle the question of a quasilinear renormalisation formula, the last remaining component of the quasilinear solution theory;
(iii) Develop an efficient quantitative approximation theory of singular SPDEs, removing the criticality barrier from the rate of convergence.
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More information & hyperlinks
| Web resources: | https://cordis.europa.eu/project/id/101117125 |
| Start date: | 01-03-2024 |
| End date: | 28-02-2029 |
| Total budget - Public funding: | 1 498 849,00 Euro - 1 498 849,00 Euro |
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Original description
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. The purpose of this project is to study a number of important questions in the field, open new directions, and challenge central open problems:(i) Launch the investigation of singular SPDEs that preserve Gibbs measures of distributional Hamiltonians such as the density of self-repellent polymers;
(ii) Tackle the question of a quasilinear renormalisation formula, the last remaining component of the quasilinear solution theory;
(iii) Develop an efficient quantitative approximation theory of singular SPDEs, removing the criticality barrier from the rate of convergence.
Status
SIGNEDCall topic
ERC-2023-STGUpdate Date
12-03-2024
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