Project description
Solving the enigma of stochastic partial differential equations
Complexities proliferate within stochastic partial differential equations (SPDEs), presenting persistent challenges across diverse domains of probability and mathematical physics. Singular equations, despite recent breakthroughs by luminaries like Hairer and Gubinelli, Imkeller and Perkowski, continue to pose new challenges, presenting unforeseen obstacles. The ERC-funded SPDE project aims to overcome this impasse through three key lines of enquiry. Specifically, these encompass unravelling the enigma of singular SPDEs preserving Gibbs measures of distributional Hamiltonians, tackling the elusive quasilinear renormalisation formula and enhancing quantitative approximation theories. By transcending critical barriers, this initiative promises to propel the understanding of SPDEs to unprecedented heights, shedding light on fundamental aspects of probability and mathematical physics.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
- natural scienceschemical sciencespolymer sciences
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
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Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Topic(s)
Funding Scheme
HORIZON-ERC - HORIZON ERC GrantsHost institution
1040 Wien
Austria