Objective
"Lie theory was created at the end of the 19th century, and rapidly became a central chapter of contemporary mathematics. Finite-dimensional Lie groups and Lie algebras were extensively studied for more than a century, and are well understood. In attempting to generalise the finite-dimensional objects, one can roughly distinguish two general approaches, one ""analytic"" (keeping the smooth manifold structure of Lie groups) and the other “algebraic” (which is best represented by the algebraic constructions of Kac-Moody groups).
Although intensively studied, Kac–Moody groups and Lie groups beyond the affine case remain mysterious to a large extent, and many questions concerning their structure remain open. In my Ph.-D. thesis, I established several structure results concerning topological Kac–Moody groups of indefinite type, and part of this research project carries on this study further. The main goal of this research project is to get a better understanding of Kac–Moody groups beyond the affine case, from both the analytic and algebraic approaches, and to try to construct “concrete realisations” of these groups (at least for hyperbolic types), by studying the unitary representations of their Lie algebra. More precisely, my method would be to try to construct certain “concrete” representations of a distinguished class of Lie algebras that include all symmetrisable Kac–Moody algebras; it should then be possible to construct “concrete realisations” of the corresponding groups by integrating these representations, hopefully allowing for an in-depth study of these groups.
This research project would allow me to significantly broaden and diversify my mathematical knowledge and experience, as I would study Kac-Moody groups and algebras from a wholly different perspective (the ""analytic"" one) and investigate its applications to theoretical physics, thus placing my research in an interdisciplinary context."
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.
- natural sciences mathematics pure mathematics algebra algebraic geometry
- natural sciences physical sciences theoretical physics
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Programme(s)
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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-2013-IEF
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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
91058 ERLANGEN
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.