Project description
Advancing long-open conjectures related to number theory and automorphic forms
Number theory, the study of whole-number relationships, and the theory of automorphic forms, a broader theory connecting algebra, geometry and analysis, have long informed each other and at the same time created a web of foundational unsolved conjectures at their intersection. The ERC-funded AuForA project will focus on three prototypical higher-rank cases: Michel and Venkatesh’s joint equidistribution conjectures for shifted complex multiplication points, Langlands’ beyond endoscopy programme on functorial lift identification, and Sarnak’s density conjectures concerning exceptional eigenvalues and their number theoretical consequences. The project will combine analytic number theory and automorphic forms in an interdisciplinary approach to achieve substantial progress on these fundamental long-standing conjectures.
Objective
This proposal is at the interface of number theory and automorphic forms and aims at a cross-fertilization of both areas. It focuses on explicit arithmetic problems that can be solved using the full force of the automorphic machinery. Conversely it develops the theory of automorphic forms in higher rank using number theoretic methods.
At the core are three sets of deep and longstanding open conjectures in higher rank cases:
- the joint equidistribution conjectures of Michel and Venkatesh concerning the distribution of pairs of shifted CM points,
- the beyond endoscopy program of Langlands of identifying functional lifts by a comparison of different trace formulae,
- the density and optimal lifting conjectures of Sarnak concerning the behaviour of exceptional eigenvalues, and their arithmetic consequences.
The key objects are certain Shimura varieties associated to abelian varieties, higher rank Kloosterman sums, families of L-functions, trace formulae and Hecke eigenvalues.
By an interdisciplinary combination of analytic number theory and automorphic forms, the proposal aims at definitive progress and solutions to these three conjectures, each of which has been open for at least 15 years.
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.1.1 - 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-2021-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.
53113 BONN
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.