Objective
This research program originates from a pressing practical need and from a purely new geometric perspective of discrete mathematics..
Graphs play a key role in many application areas of mathematics, providing the perfect mathematical description of all systems that are governed by pairwise interactions, in computer science, economics, biology and more. But graphs cannot fully capture scenarios in which interactions involve more than two agents. Since the theory of hypergraphs is still too under-developed, we resort to geometry and topology, which view a graph as a one-dimensional simplicial complex. I want to develop a combinatorial/geometric/probabilistic theory of higher-dimensional simplicial complexes. Inspired by the great success of random graph theory and its impact on discrete mathematics both theoretical and applied, I intend to develop a theory of random simplicial complexes.
This combinatorial/geometric point of view and the novel high-dimensional perspective, shed new light on many fundamental combinatorial objects such as permutations, cycles and trees. We show that they all have high-dimensional analogs whose study leads to new deep mathematical problems. This holds a great promise for real-world applications, in view of the prevalence of such objects in application domains.
Even basic aspects of graphs, permutations etc. are much more sophisticated and subtle in high dimensions. E.g. it is a key result that randomly evolving graphs undergo a phase transition and a sudden emergence of a giant component. Computer simulations of the evolution of higher-dimensional simplicial complexes, reveal an even more dramatic phase transition. Yet, we still do not even know what is a higher-dimensional giant component.
I also show how to use simplicial complexes (deterministic and random) to construct better error-correcting codes. I suggest a new conceptual approach to the search for high-dimensional expanders, a goal sought by many renowned mathematicians.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics topology
- natural sciences computer and information sciences
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics applied mathematics mathematical model
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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.
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.
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.
ERC-2013-ADG
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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.
Host institution
91904 JERUSALEM
Israel
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.