Objective
Infinite graphs and their combinatorics model large real-life networks, like the internet, but are also an essential tool to understand mathematical structures that are intrinsically infinite, like the geometry of the Euclidean spaces. The project concerns research in descriptive set theory and its interactions with measure theory, dynamical systems, graph limits and theoretical computer science through the study of regularity properties of combinatorial problems on infinite graphs. These considerations played a fundamental role in the spectacular results on the circle squaring problem and form a new field, measurable graph theory.
In the last years, an explosion of activity has brought new exciting ideas to this field: formal connections with the theory of distributed computing and random processes, the notion of asymptotic dimension from geometric group theory, or a generalization of the determinacy method of Marks. These ideas have already found several groundbreaking applications and are highly promising in gaining new perspectives on old problems. We propose to employ, combine and further develop these methods with particular emphasis on applications to the study of central questions of descriptive set theory, that is, Borel hyperfiniteness, equidecomposition problems, or the abstract classification problem, as well as on finding new links and applications to classical graph theory, in particular, to algorithmic aspects of partition problems on finite graphs.
The fellowship will be carried out over 26 months: 14 at UCLA, 6 at MU and 6 at Leipzig University. The supervisors, Itay Neeman at UCLA and Dan Kráľ, currently at Masaryk University and moving to Leipzig University in April 2025, are leading figures in their respective fields of interest, descriptive set theory and combinatorics. Together with the expertise of the fellow, the project promises a unique potential for bridging these fields, solving deep problems in both areas, developing the fellow's research profile and bringing the contemporary trends of descriptive set theory to Central Europe.
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.
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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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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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.
HORIZON-TMA-MSCA-PF-GF - HORIZON TMA MSCA Postdoctoral Fellowships - Global Fellowships
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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) HORIZON-MSCA-2022-PF-01
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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.
04109 Leipzig
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.