Project description
Research could offer clues to key questions on smooth ergodic theory and dynamical systems
The EU-funded Resonances project plans to develop new, original methods to address a number of fundamental questions regarding smooth ergodic theory and dynamical systems. The newly proposed methods should find applications in different areas of mathematics, in particular geometry, number theory and topology. The questions under study are specifically related to resonances, which characterise statistical properties of dynamical systems through the correlation function and the zeta function. The project aims to develop a new theory of resonances and correlation functions for a broader class of systems that are currently not being addressed by any existing theories.
Objective
The objective of this research project is to develop new and original methods to address a number of fundamental questions in the development of smooth ergodic theory and dynamical systems. Furthermore, this theory will have important and diverse applications to many different areas of mathematics (in particular geometry, but also number theory and topology).
The questions we are interested in are specifically related to the study of resonances, which characterise statistical properties of dynamical systems via the correlation function and the zeta function.
The generality of the approach draws heavily on the PI's experience with the ergodic theory of hyperbolic systems, an area of research in which the PI has played a leading role for many years, but the risk and ambition stems from the novelty and risk inherent in trying to apply new ideas.
There are three major strands to this work although they are bound together by interactions both at the level of the conclusions and the methodology.
(a) The first is the development of new methods for determining numerically basic characteristic values, which are theoretically poorly understood, for classical (``chaotic'') hyperbolic systems. The important new development is a completely rigorous estimate on the approximation.
(b) The second main theme will be the establishment of a radically new theory of resonances and correlation functions for a broader classes of systems, for which there is presently no existing theory. Typically these examples arise in geometry, and will help advancing our understanding of problems in that area.
(c) The third main topic will be applications to specific major problems, particularly in hyperbolic geometry, and number theory.
A key ingredient in our approach is the blending of classical ideas from classical thermodynamic formalism with more progressive functional analytic techniques that continue to emerge.
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.
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
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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)
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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.
CV4 8UW COVENTRY
United Kingdom
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.