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Additive Combinatorics and Higher-Order Fourier Analysis in Number Theory

Objetivo

Additive combinatorics is the name given to the part of mathematics which has grown out of the study of certain basic questions about finite sets of integers. For example, which conditions on a set of integers guarantees that it contains an arithmetic progression of a given length k?

The particular set of tools at the core of my proposal falls under the name Higher-order Fourier analysis, a generalisation of classical harmonic analysis in which nilpotent groups join abelian groups as the key underlying structures.

My proposal aims to further develop basic theory, particularly related to Higher-Order Fourier Analysis, but also to other parts of additive combinatorics, and use such developments to prove results of number-theoretic interest.

Ámbito científico (EuroSciVoc)

Palabras clave

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Tema(s)

Régimen de financiación

HORIZON-ERC - HORIZON ERC Grants

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Convocatoria de propuestas

(se abrirá en una nueva ventana) ERC-2025-ADG

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Institución de acogida

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Aportación neta de la UEn
€ 2 499 723,00
Dirección
WELLINGTON SQUARE UNIVERSITY OFFICES
OX1 2JD Oxford
Reino Unido
Región
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Tipo de actividad
Higher or Secondary Education Establishments
Enlaces
Coste total
Sin datos

Beneficiarios (1)