Project description
An interdisciplinary approach to the study of discrete dynamical systems
Discrete dynamical systems are mathematical models used in many fields including computer science and biology, to study how systems change over time. While they seem simple to describe, they give rise to compelling open problems. One such example is the Skolem Problem, which asks if a dynamical system ever hits a given hyperplane. The EU-funded DynAMiCs project will combine tools from different areas of mathematics and computer science such as number theory and logic to study discrete dynamical systems. The project will combine expertise in number theory, symbolic dynamics and mathematical logic.
Objective
Discrete dynamical systems pervade the quantitative sciences, and lie at the heart of central computational challenges in a wide variety of areas, from program analysis and computer-aided verification to neural networks and theoretical biology. Such systems are typically simple to describe, yet give rise to a rich algorithmic and mathematical theory that is replete with easily stated and compelling open problems. One such example is the famous Skolem Problem: does the orbit of a given linear dynamical system ever hit a given hyperplane? The decidability of this question is a longstanding open problem going back nearly a century!
The main goal DynAMiCs is to achieve major advances in the algorithmic theory of discrete linear dynamical systems and related formalisms. Whilst our motivation and outlook originate from computer science and automated verification, we approach these challenging problems from both mathematical and computational angles, combining tools and techniques from number theory (e.g. Diophantine approximation, transcendence theory, continued fractions), symbolic dynamics (e.g. word combinatorics, subshifts, numeration systems), and mathematical logic (e.g. monadic second-order logic, Presburger arithmetic, automata theory). One of our leading objectives is to substantially broaden the classes of dynamical systems and properties that can be algorithmically handled via model checking. We aim to achieve these ambitious advances by pursuing new approaches to central open problems in linear systems, such as the Skolem Problem, building on recent breakthroughs in these areas (some of which from the PIs and their groups).
We take on this challenge with a team of PIs consisting of international leaders in algorithmic verification, symbolic dynamics, and analytic number theory. We believe our complementary expertise places us in a unique position to achieve major breakthroughs in longstanding fundamental problems in the area of discrete dynamical systems.
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 arithmetics
- 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)
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.
HORIZON-ERC-SYG - HORIZON ERC Synergy 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-SyG
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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.
80539 MUNCHEN
Germany
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.