Project description
Exploring links between multiplicative number theory and additive combinatorics
Multiplicative number theory is an area of number theory dealing with prime numbers and multiplicative functions. One of the great open questions in the field is Chowla's conjecture, which states that the prime factorizations of consecutive numbers should behave independently of each other. Funded by the Marie Skłodowska-Curie Actions programme, the MultNT project aims to more thoroughly study Chowla’s conjecture, as well as other key questions in multiplicative number theory. This project will also explore connections between Chowla’s conjecture and additive combinatorics and higher-order Fourier analysis. Furthermore, MultNT will focus on the Hardy-Littlewood conjecture on average and the Hasse principle for almost all surfaces of a certain type.
Objective
This project concerns multiplicative number theory and its interplay with the emerging topic of additive combinatorics. Multiplicative number theory is an area of number theory concerned with the study of prime numbers and multiplicative functions. One of the most important unsolved questions in this area and in all of number theory is the twin prime conjecture, asserting that there are infinitely many pairs of prime numbers differing by two.
In 1965, Chowla formulated an influential conjecture that can be viewed as an approximation to the twin prime conjecture. Chowla’s conjecture predicts that the prime factorisations of consecutive integers behave independently of each other. This conjecture captures the key difficulty in the twin prime conjecture, but yet there has been a lot of recent progress on Chowla’s conjecture by the applicant and others.
The aim of this project is to make substantial progress on Chowla’s conjecture, as well as on other key questions in multiplicative number theory, using a mixture of methods from analytic number theory and additive combinatorics, as well as higher order Fourier analysis, a theory recently developed by Green and Tao. Connections between Chowla’s conjecture and questions in additive combinatorics and higher order Fourier analysis have recently been discovered in works of the applicant and others, and the proposed research aims at exploiting these connections to make substantial progress on Chowla’s conjecture. The project also involves several other problems of interest in number theory, such as the Hardy—Littlewood conjecture on average and the Hasse principle for almost all surfaces of a certain type.
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 discrete mathematics combinatorics
- natural sciences mathematics pure mathematics arithmetics prime numbers
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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.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2021-PF-01
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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.
20014 Turku
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.