Project description
Understanding the Langlands correspondence at higher dimensions
The Langlands correspondence has been crucial in solving many challenging mathematical problems. It consists of a series of mathematical predictions describing a deep relationship between discrete and continuous mathematics, two fundamental branches underpinning counting, number theory, and analysis. However, despite numerous advances, understanding of the Langlands correspondence remains limited. Supported by the Marie Skłodowska-Curie Actions programme, the LGModGal project will develop a framework to better control the underlying geometric spaces involved in this approach to the correspondence. By combining representation theory and algebraic geometry techniques, the project will enable the study of the correspondence in dimensions higher than two.
Objective
The Langlands correspondence is a series of mathematical predictions describing a deep relationship between
two fundamental branches of mathematics: discrete mathematics, which is the basis of counting and number
theory, and continuous mathematics, which underlies analysis. These connections are incredibly powerful and have helped solve some of the most challenging problems in mathematics, such as Fermat's Last Theorem, which remained unsolved for nearly 400 years.
Despite significant advances over the past 30 years, much of this area remains unexplored. Recently, a new approach has emerged with the potential to revolutionise our understanding of the Langlands correspondence. The expectation is that this correspondence can be achieved via an interpretation of the analytic side as functions on geometric spaces which are built from basic objects on the discrete side—specifically symmetries of solutions to polynomial equations like Y²=X³+X+1. While it is speculated that this viewpoint will substantially simplify the problem, it is presently unclear how exactly these ideas should be implemented. A major issue is that the underlying geometry of these spaces are hard to control, rendering a precise interpretation as functions difficult.
My research has hinted that, through innovative combinations of techniques from algebraic geometry and representation theory, taming this geometry is within reach. In this project I will develop these ideas to produce a general framework which controls these spaces. Consequently, foundational results in the Langlands correspondence, currently limited to dimension 2, will be developed in higher dimensions, making inroads into one of the most important and enduring problems of 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.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
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.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
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
See all projects funded under this funding scheme
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-2024-PF-01
See all projects funded under this callCoordinator
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.
E1 4NS LONDON
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.