Objective
During his construction of a solid mathematical theory behind - the at that time completely new - quantum mechanics, von Neumann introduced his eponymous algebras to describe observable quantities. These “von Neumann algebras” became a basic tool in various other branches of mathematics, including Lie theory (the theory of continuous symmetries), non-commutative geometry (a “quantum” version of classical differential geometry), and, surprisingly, the theory of knots, for which V. Jones received a Fields Medal.
Strangely enough, although the theory of von Neumann algebras is quite pervasive in mathematics and mathematical physics, their actual construction and classification remains largely shrouded in mystery (despite deep work on classification by A. Connes, also getting him a Fields Medal). Particularly unsatisfactory is that the types of von Neumann algebras that are most relevant to quantum mechanics, so-called “type III”-algebras, are very rare.
With this Marie-Curie fellowship, I pick up the two challenges of construction and classification, especially focussing on Connes' famous rigidity conjecture for lattices in Lie groups as well as type III von Neumann algebras, using two entirely new approaches. The first is the use of finite-dimensional approximations, that I used previously in a different context (studying the Haagerup property and Lp-Fourier multipliers). The second new approach is based on the theory of quantum groups.
Utrecht University (host institution) is the unique place in Europe housing both experts in non-commutative analysis and Lie theory, and thereby provides exactly the necessary (complementary) expertise that is necessary to attack these deep and profound problems.
The results will have a lasting impact on and connect further the theories of non-commutative geometry, operator algebras, Lie theory, quantum group theory and partly quantum physics.
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 physical sciences quantum physics
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences mathematics pure mathematics mathematical analysis functional analysis operator algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2015
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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.
3584 CS Utrecht
Netherlands
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.