Project description
Mathematical models to explain natural phenomena: tomography, turbulence and random tilings
Scaling invariance occurs in different forms in many natural phenomena. A well known example of a rough scale invariance is the fractal nature of a shoreline. From a mathematical point, explaining and making use of the scale invariance leads to the method of conformal (shape preserving) and quasiconformal mappings (that preserve shapes only roughly). Fourier analysis, where one decomposes a signal into its constituent frequencies, provides a related approach to analyse complicated natural phenomena. QUAMAP is devoted to applying aspects of modern mathematical analysis, from quasiconformal mappings to Fourier analysis, to several problems arising in mathematical physics. Using these tools, along with nonlinear analogues, the project hopes to shed light on diverse challenging problems including the geometry of energy minimisers, scaling limits in random geometry, an imaging technique based on electrical surface measurements, as well as the behaviour of fluids in turbulent regimes.
Objective
The use of delicate quasiconformal methods, in conjunction with convex integration and/or nonlinear Fourier analysis, will be the common theme of the proposal. A number of important outstanding problems are susceptible to attack via these methods. First and foremost, Morrey's fundamental question in two dimensional vectorial calculus of variations will be considered as well as the related conjecture of Iwaniec regarding the sharp $L^p$ bounds for the Beurling transform. Understanding the geometry of conformally invariant random structures will be one of the central goals of the proposal. Uhlmann's conjecture regarding the optimal regularity for uniqueness in Calder\'on's inverse conductivity problem will also be considered, as well as the applications to imaging. Further goals are to be found in fluid mechanics and scattering, as well as the fundamental properties of quasiconformal mappings, interesting in their own right, such as the outstanding deformation problem for chord-arc curves.
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.
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.
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. 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.
Funding scheme (or “Type of Action”) inside a programme with common features. 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.
ERC-ADG - Advanced Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2018-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
00014 HELSINGIN YLIOPISTO
Finland
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.