Additive Combinatorics Higher Tender

ACHOFAINT
Grant agreement ID: 101265009

DOI
10.3030/101265009

EC signature date
20 August 2026
Start date
1 August 2027
End date
31 July 2032
Funded under
European Research Council (ERC)
Objective

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.