Objective
Prime numbers have fascinated mathematicians for centuries, and have given rise to some of the oldest and most notorious open problems. Despite their central status, many fundamental aspects of the primes remain beyond the reach of current techniques.
This project aims to make progress on central questions related to the distribution of primes. The goal is to develop new versatile techniques that can provide inroads to the fundamental problems at the heart of the subject, building on recent breakthroughs of the PI.
There are two key approaches to studying the distribution of primes. ‘Multiplicative’ techniques relate structured questions to the zeros of an L-function. The strength of results typically depends on progress toward the Riemann Hypothesis, but these techniques work well on questions with special structure connected to L-functions. In contrast ‘additive’ techniques use sieve methods to study primes. They have the advantage of being very flexible, but often cannot give a strong a result on their own. In favourable situations, additive techniques (particularly ‘Type I/II sums’) can be used to reduce an ‘unstructured’ question about primes to a ‘structured’ one, which can then be solved using multiplicative techniques.
This project aims to further our understanding of both the ‘multiplicative’ techniques related to L-functions and the ‘additive’ techniques connected to prime-detecting sieves, as well as the links between them.
A common theme of the project is to classify barriers to progress, and then develop new techniques to rule out such a barrier. This involves using ideas from other areas—such as combinatorics, geometry, probability, automorphic forms, and harmonic analysis—to create new tools to address these challenges. The proposal outlines a series of intermediate problems designed to test and develop these new methods, demonstrating the power of novel approaches to break through long-standing historical barriers in questions related to primes.
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
- natural sciences mathematics pure mathematics arithmetics prime numbers
- natural sciences mathematics pure mathematics arithmetics L-functions
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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 - 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-2025-COG
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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.
OX1 2JD Oxford
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.