Objective
The proposed research of this proposal is in algebraic Lie theory and Poisson geometry, two fields of pure mathematics with strong interactions with other sciences including computing science, chemistry, physics and economics.
In recent works, the applicant developed new techniques from combinatorics/graph theory in order to study the representation theory of quantised coordinate rings, whereas the host has been developing algorithmic methods in order to study the representation theory of these noncommutative algebras.
A motivating factor for the existence of this project is the desire to unite these disparate approaches to the study of quantum algebras in the hope that rapid and deep progress can then be made. That this is feasible is supported by three recent articles of the applicant and the host where combining their techniques led to the solution of a long-awaited results on the dimension of certain algebraic varieties appearing in the context of quantum algebras.
More precisely, the aim of this project is to combine the techniques developed by the applicant on one hand, and by the host on the other hand, in order to fully understand the space of primitive ideals of certain class of noncommutative algebras of current interests such as quantum (affine) Schubert cells, quantum flag varieties, quantum cluster algebras. In addition, the geometric properties (normality, AS Cohen-Macaulay, AS Gorenstain...) of the prime/primitive quotients will be studied in the spirit of noncommutative algebraic geometry.
All of the noncommutative algebras mentioned are actually deformations of classical varieties, and so these algebras are algebraic deformations of certain Poisson varieties. The second main aim of the project is to use these new techniques in order to understand the link between the primitive ideals of these noncommutative algebras with the symplectic leaves of their semi-classical limits.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- social sciences economics and business economics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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.
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.
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.
FP7-PEOPLE-2012-IIF
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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.
Coordinator
CT2 7NZ Canterbury, Kent
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.