Objective
Quantum affine algebras are important examples of Drinfeld-Jimbo quantum groups. They can be defined as quantizations
of affine Kac-Moody algebras or as affinizations of finite type quantum groups (Drinfeld Theorem).
The representation theory of quantum affine algebras is very rich. It has been studied intensively during the past twenty five
years from different point of views, in particular in connections with various fields in mathematics and in physics, such as
geometry (geometric representation theory, geometric Langlands program), topology (invariants in small dimension),
combinatorics (crystals, positivity problems) and theoretical physics (Bethe Ansatz, integrable systems).
In particular, the category C of finite-dimensional representations of a quantum affine algebra is one of the most studied
object in quantum groups theory. However, many important and fundamental questions are still unsolved in this field. The aim of the research project is to make significant advances in the understanding of the category C as well as of its applications in the following five directions. They seem to us to be the most promising directions for this field in the next years :
1. Asymptotical representations and applications to quantum integrable systems,
2. G-bundles on elliptic curves and quantum groups at roots of 1,
3. Categorications (of cluster algebras and of quantum groups),
4. Langlands duality for quantum groups,
5. Proof of (geometric) character formulas and applications.
The resources would be used for the following :
(1) Hiring of 2 PhD students (in 2015 and 2017).
(2) Hiring of 2 Postdocs (in 2015 and 2017).
(3) Invitations and travel for ongoing and future scientific collaborations.
(4) Organization of a summer school in Paris on quantum affine algebras.
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 topology
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences physical sciences theoretical physics
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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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H2020-EU.1.1. - EXCELLENT SCIENCE - 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.
ERC-COG - Consolidator Grant
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2014-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.
75794 Paris
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.