Project description
A cross-disciplinary approach to studying random complexes and graph limit theory
Graph limit theory is a branch of mathematics that enables researchers to study large, complex networks by representing them as continuous objects known as graphons. With the support of the Marie Skłodowska-Curie Actions programme, the RaCoCoLe project will use this theory to explore random simplicial complexes – geometric structures that help understand higher-dimensional spaces. By connecting this with questions about random integral matrices (inspired from number theory), the proposed study plans to transfer insights between these fields. Furthermore, it will explore how these complexes expand and behave in random settings. Building on previous research, the study will also introduce new applications, such as in stochastic topology (the study of randomness in shapes), and open new directions in graph limit theory.
Objective
Graph limit theory is a rapidly developing field of mathematics. Mészáros proposes to use ideas from graph limit theory to answer questions about random simplicial complexes. The motivation for investigating the cokernels of random integral matrices comes from the number theoretic conjectures of Cohen and Lenstra. Mészáros plans to make use of the fact that the questions arising studying the homology of random simplicial complexes are very similar to questions about the cokernels of random integral matrices. Thus, ideas can be transferred from one area to the other. Mészáros also proposes to investigate the expansion properties of random simplicial complexes.
Many researchers at the Rényi Institute (the host institute) played a key role in developing graph limit theory and finding applications of this theory in several areas including ergodic theory, group theory, probability theory, statistical physics and computer science. Large part of Mészáros’s past and proposed projects relies on these techniques. Building on the research that he started during his three years at the University of Toronto as a postdoctoral fellow, Mészáros will bring new questions and areas where these techniques can be applied like stochastic topology. Mészáros’s work will not only provide new areas of applications, but hopefully will open new directions in graph limit theory. The arising new topics in graph limit theory can be of great interest to many members of the host institute.
The fellowship would provide Mészáros an excellent opportunity for many fruitful collaborations to explore these topics further. He is also looking forward to improving his organization, management and communication skills to become a more well rounded researcher.
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 mathematics pure mathematics topology
- natural sciences mathematics applied mathematics statistics and probability
- natural sciences computer and information sciences artificial intelligence heuristic programming
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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)
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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)
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Topic(s)
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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
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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-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2024-PF-01
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1053 Budapest
Hungary
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