Objective
The project GalRep-EllCrv builds on Lorenzo Furio’s PhD thesis, where he achieved breakthroughs in the study of Galois representations attached to elliptic curves. This classical field has been central to major advances in number theory, including the proof of Fermat’s Last Theorem. The project addresses problems linked to Serre’s uniformity question, a long-standing challenge at the heart of the field.
The research is structured into three directions:
[A] Develop faster methods to compute integral points on non-split Cartan modular curves, correcting and extending previous results and pushing the limits of computational techniques.
[B] Complete the classification of 7-adic Galois representations, a cornerstone of Mazur’s Program B, by resolving a specific genus-3 curve and creating new algorithms with broader applications.
[C] Prove the first uniform bound on Serre’s constant, a measure of hidden symmetries in elliptic curves, with wide implications for Diophantine geometry.
Beyond its scientific goals, the project will advance open science by releasing code and results openly, foster dissemination through publications, talks, and outreach, and promote societal reflection by integrating ethics into mathematical events. The applicant’s ongoing engagement with the Mathematical Olympiads will further inspire younger generations and encourage diversity in mathematics.
The fellowship will be hosted at the University of Bordeaux, under the supervision of Pierre Parent, a world leader in the study of elliptic and modular curves. The combination of the applicant's recent breakthroughs with the host's expertise will provide an ideal environment for this ambitious project and position the applicant at the forefront of research in modern number theory.
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.
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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-2025-PF
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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.
33000 BORDEAUX
France
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.