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Find similar grantsOvercoming criticality for PDEs with randomness is sponsored by European Research Council (ERC). This ERC project aims to address criticality in partial differential equations with randomness, relevant to stochastic modeling in financial mathematics.
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Overcoming criticality for PDEs with randomness Answering questions of PDEs and dispersive equations Differential equations are fundamental to many fields, enabling critical calculations and insights. The study of partial differential equations (PDEs), particularly dispersive equations, has seen increasing focus and interest due to their potential in advancing fields such as quantum field theory.
Unfortunately, despite recent key breakthroughs in the theory of singular stochastic parabolic PDEs, many key questions of dispersive equations remain unanswered. The ERC-funded CritPDEsRand project aims to develop mathematical tools and concepts to explore these fundamental problems.
Specifically, the project will use advances in probability and the interface of the two fields to deduce critical insights and overcome previous challenges. Show the project objective Hide the project objective "This proposal is concerned with the study of the dynamics of partial differential equations (PDEs), broadly interpreted, in the presence of randomness, with a particular focus on dispersive equations.
This is a young but promising emerging field, and it has deep connections with the more established field of constructive quantum field theory. In recent years, we have witnessed outstanding advances in the theory of singular stochastic parabolic PDEs, and while several breakthroughs have been obtained for the dispersive counterpart, many fundamental questions are still open.
In particular, many of these questions are ""critical"" or ""supercritical"" according to our current understanding. The main goal of this proposal is to develop novel mathematical ideas and tools to break this barrier of criticality, and provide a resolution to these fundamental problems. Over the last ten years, there has been significant progress at the interface of dispersive PDEs and probability.
In my short career, I have been one of the leading figures of this field and I have achieved significant breakthroughs. Particularly, my works on phase transitions for focusing Gibbs measures, ergodicity results for stochastic wave equations and global well posedness result for fractional NLS in negative regularity have opened the door to new exciting possibilities. 1.
I will work on the Φ^p_d quantum field theories on R^d, both in the focusing and defocusing regime. This will answer major open questions related to the soliton resolution conjecture and in constructive quantum field theory. 2.
I will improve our understanding of how Gaussian measures are transported by the flow of nonlinear PDEs. 3. I will develop a theory of (regular) Lagrangian flows for dispersive PDEs, and use it to break the barrier of criticality for these equations."
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. See: The European Science Vocabulary . partial differential equations Suggest new fields of science Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums. HORIZON-ERC - HORIZON ERC Grants See all projects funded under this funding scheme Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding. See all projects funded under this call Net EU financial contribution.
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OLD COLLEGE, SOUTH BRIDGE Higher or Secondary Education Establishments Participation in EU R&I programmes HORIZON collaboration network The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget. Download Download the content of the page Last update: 20 October 2025 Permalink: https://cordis.
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According to the current listing, eligibility includes: Open to researchers and institutions within the European Union. Confirm the full requirements in the official notice before applying.
The current listing shows €1,496,455. Verify award ceilings, matching requirements, and allowable costs in the official notice.
Overcoming criticality for PDEs with randomness is funded by European Research Council (ERC). Verify program details on the funder's official page before applying.
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MGPV Travel Grant is sponsored by Geological Society of America (GSA), Mineralogy, Geochemistry, Petrology, Volcanology Division. MGPV Travel grants support student travel to the annual GSA meeting. Applications are restricted to active graduate or undergraduate students who are the presenting authors of an accepted abstract at the annual GSA meeting.
Research Opportunities in Space and Earth Science (ROSES) - 2025: A.4 Rapid Response and Novel Research in Earth Science is sponsored by National Aeronautics and Space Administration (NASA) Science Mission Directorate (SMD). This omnibus research funding opportunity includes various program elements, with rolling submissions for Earth Science research through August 2026. Proposers to Earth Science using the NASA Center for Climate Simulation high-end computing facility must include specific budget details.