Project description
Advancing dynamical systems and creating novel insights
The field of dynamical systems (founded by Poincaré during his study of the N-body problem) has seen remarkable progress and breakthroughs in recent years. These advances benefit the field itself, in addition to areas as diverse as theoretical computer science, combinatorics, and number theory. In fact, new findings in dynamical systems continue to provide critical insights across the sciences. With this in mind, the ERC-funded DyAddAlg project will explore several central open problems in the field, with a particular focus on multidimensional averages in ergodic theory, additive combinatorics, and other key areas.
Objective
The last two decade have witnessed a new spring for dynamical systems. The field - initiated by Poincare in the study of the N-body problem - has become essential in the understanding of seemingly far off fields such as combinatorics, number theory, and theoretical computer science. In particular, ideas from ergodic theory played an important role in the resolution of long standing open problems in combinatorics and number theory. A striking example is the role of dynamics on nilmanifolds in the proof of Hardy-Littlewood estimates for the number of solutions to systems of linear equations of finite complexity in the prime numbers. The interplay between ergodic theory, number theory and additive combinatorics and very recently also algebraic geometry has proved very fruitful; it is a fast growing area in mathematics attracting many young researchers. I propose to tackle a wide range of central open problems in the area, focusing on multidimensional averages in ergodic theory and additive combinatorics, the stability phenomena for polynomial rings in many variables, and randomness properties of arithmetic functions.
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 geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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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HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2024-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.
91904 Jerusalem
Israel
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