SubsidieMeestersHigh Dimensional Probability and Combinatorics
This project aims to explore random matrices, hypergraph Ramsey numbers, and the Chowla cosine problem using high-dimensional probability and combinatorial methods.
Projectdetails
Introduction
This project concerns three related topics concerning high dimensional probability and combinatorics.
Random Matrices
The first part concerns fundamental questions regarding random matrices. These include:
- The problem of finding sharp bounds on the singularity probabilities for discrete random matrices.
- Determining the limiting spectral distributions of "sparse" matrix models.
Hypergraph and Multi-colour Ramsey Numbers
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.
Chowla Cosine Problem
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.
Financiële details & Tijdlijn
Financiële details
| Subsidiebedrag | € 1.499.408 |
| Totale projectbegroting | € 1.499.408 |
Tijdlijn
| Startdatum | 1-11-2024 |
| Einddatum | 31-10-2029 |
| Subsidiejaar | 2024 |
Partners & Locaties
Projectpartners
- THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGEpenvoerder
Land(en)
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This project explores integrable probability by applying advanced mathematical methods to stochastic models, aiming to derive precise limit theorems and enhance understanding of random walks and representations.
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