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Randomness and pseudorandomness in discrete mathematics

Objectif

Discrete mathematics has seen enormous advances in the last few years, with solutions being found to a number of famous and long-standing questions, such as the Erdos distinct distance problem and the existence conjecture for combinatorial designs. Much of this progress owes to an increased understanding of random and pseudorandom objects. An entire framework, known as the probabilistic method, has grown around the application of randomness to combinatorial problems, while pseudorandomness is playing an increasingly important role.

In this proposal, we will consider a range of problems, some stemming from the direct study of random and pseudorandom objects and others arising in areas where randomness and pseudorandomness have proved to be of particular importance. We will be particularly concerned with extensions of the regularity method to sparse graphs and improving bounds for a number of classical problems in graph Ramsey theory. These problems are of a fundamental nature and any progress is likely to lead to new techniques with broader scope for application.

Mots‑clés

Régime de financement

ERC-STG - Starting Grant

Institution d’accueil

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Contribution nette de l'UE
€ 1 106 719,00
Adresse
WELLINGTON SQUARE UNIVERSITY OFFICES
OX1 2JD Oxford
Royaume-Uni

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Région
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Type d’activité
Higher or Secondary Education Establishments
Liens
Coût total
€ 1 106 719,00

Bénéficiaires (1)