Project description
Study could offer new insight on problems central to graphs and hypergraphs
Combinatorics is primarily concerned with problems of selection, arrangement and operation within discrete systems. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, evolutionary biology and computer science. The EU-funded GeoScape project aims to tackle certain problems for large classes of graphs and hypergraphs arising in geometry and algebra. These fundamental structures escape the ‘curse of dimensionality’: they can either be embedded in a bounded-dimensional space, or have a small VC-dimension, or a short algebraic description. The insight gained could lead closer to the solution of certain classical problems, such as the Erdős-Hajnal conjecture, and to the design of improved algorithms for clustering and property testing in huge graphs.
Objective
"Combinatorics is a fundamental mathematical discipline whose study has experienced unprecedented growth during the past few decades. Its rapid development can be partially explained by spectacular applications of extremal combinatorics in additive number theory, information theory, theoretical computer science, and elsewhere. Asymptotic results in extremal and probabilistic combinatorics have proved to be powerful tools in the structural and algorithmic analysis of huge networks such as the internet graph, brain maps, social networks, and integrated circuits. We have deep, well developed algebraic, topological, and probabilistic techniques to tackle some basic problems of modern combinatorics, but many classic Ramsey-, Turn-, and Szemerdi-type questions remained open.
The main goal of the proposed work is to attack some hard problems for large classes of graphs and hypergraphs arising in geometric, algebraic, and practical applications. These structures escape the ""curse of dimensionality: they can be embedded in a bounded-dimensional space, or they have small VC-dimension, or a short algebraic description. The work of the principal investigator, his collaborators and students has played a significant role in the introduction of modern combinatorial tools in geometry. In the present project, he aims to explore the reverse direction: to develop and apply geometric techniques to settle important special cases of notoriously difficult combinatorial problems on (1) bounded degree semi-algebraic graphs and hypergraphs, (2) graphs and hypergraph of bounded VC-dimension, (3) ordered graphs, 0-1 matrices, and graphs embedded in the plane or in other surfaces. Progress on the problems described in the proposal is expected to lead closer to the solution of some classical problems such as the Erds-Hajnal conjecture, the Danzer-Rogers conjecture, the Schur-Erds problem, and to the development of improved algorithms for clustering and property testing in huge graphs."
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 computer and information sciences internet
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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)
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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.
ERC-ADG - Advanced Grant
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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) ERC-2019-ADG
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1053 Budapest
Hungary
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