About:

The past decade has seen tremendous advances in the theory of Diophantine equations, arithmetic combinatorics and harmonic analysis. Moreover, influential perspectives, analogies and novel connections between these fields have developed. All of these advances are recent enough that their full potential has yet to be unleashed. Following an extended period of restricted travel, the time is ripe to unite and to push these boundaries. Our objectives for this conference were:

• To bring the harmonic analysis, number theory and arithmetic combinatorics communities all together for the first time in a conference;
• To unify these recent developments across all three areas, and explore their full scope;
• To discuss recent, highly influential applications and explore new ones;
• To assist early career researchers by connecting them to each other and to leading figures. As part of this, there was an accompanying two-day workshop for early career researchers held at ICMS, 19-20 June 2025 - Diophantine Equations, Combinatorics, Analysis in Number Theory: Emerging Researchers

Another objective was to celebrate Trevor Wooley’s revolutionary contributions across these three areas. Trevor has been an inspirational leader in these fields for decades, and many of us would relish the opportunity to reflect on his ongoing breakthrough work.

Mathematika Special Issue:

We are pleased to announce that Mathematika will publish a special issue in honour of Trevor Wooley, edited by Bob Vaughan and Joerg Brüdern. We warmly encourage all participants to consider contributing. Submissions can be made here and any queries should be directed to mathematika@lms.ac.uk. Please note that all submissions will be refereed.