Objective
One of the main challenges in condensed matter physics is to understand strongly correlated quantum systems. Our purpose is to approach this issue from the point of view of rigorous mathematical analysis. The goals are twofold: develop a mathematical framework applicable to physically relevant scenarii, take inspiration from the physics to introduce new topics in mathematics. The scope of the proposal thus goes from physically oriented questions (theoretical description and modelization of physical systems) to analytical ones (rigorous derivation and analysis of reduced models) in several cases where strong correlations play the key role.
In a first part, we aim at developing mathematical methods of general applicability to go beyond mean-field theory in different contexts. Our long-term goal is to forge new tools to attack important open problems in the field. Particular emphasis will be put on the structural properties of large quantum states as a general tool.
A second part is concerned with so-called fractional quantum Hall states, host of the fractional quantum Hall effect. Despite the appealing structure of their built-in correlations, their mathematical study is in its infancy. They however constitute an
excellent testing ground to develop ideas of possible wider applicability. In particular, we introduce and study a new class of many-body variational problems.
In the third part we discuss so-called anyons, exotic quasi-particles thought to emerge as excitations of highly-correlated quantum systems. Their modelization gives rise to rather unusual, strongly interacting, many-body Hamiltonians with a topological content. Mathematical analysis will help us shed light on those, clarifying the characteristic properties that could ultimately be experimentally tested.
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 condensed matter physics
- natural sciences mathematics pure mathematics mathematical analysis
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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.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
ERC-STG - Starting Grant
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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) ERC-2017-STG
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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.