Project description
High-dimensional probability and combinatorics interconnected topics
High-dimensional probability provides essential theoretical tools for data science, while combinatorics is widely applied in communication networks, cryptography, network security and more. With this in mind, the ERC-funded HighDimProbComb project will investigate three interconnected topics in high-dimensional probability and combinatorics. First, it will address fundamental questions about random matrices, including precise bounds on singularity probabilities and the limiting spectral distributions of sparse matrix models. Second, the project aims to advance understanding of hypergraph and multi-colour Ramsey numbers, which remain challenging despite extensive study. Finally, it will examine the Chowla cosine problem from a probabilistic perspective, an enduring question in harmonic and Fourier analysis.
Objective
This project concerns three related topics concerning high dimensional probability and combinatorics. The first part concerns fundamental questions concerning
random matrices. These include the problem of finding sharp bounds on the singularity probabilities for discrete random matrices; and determining the limiting spectral distributions of ``sparse'' matrix models.
The second major goal of this project is to make progress on the hypergraph Ramsey numbers and the multi-colour Ramsey numbers. These are two absolutely central objects in combinatorics which remain mysterious in many respects, despite many years of intense activity.
Finally, I propose to study the Chowla cosine problem. This is an old problem in the area of harmonic and Fourier analysis which the PI has recently been studying through a probabilistic lens.
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 discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
You need to log in or register to use this function
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.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
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-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
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-2024-STG
See all projects funded under this callHost institution
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.
CB2 1TN CAMBRIDGE
United Kingdom
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.