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 are:

• 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 is an accompanying two-day workshop for early career researchers to be held at ICMS, 19-20 June 2025. Please see this link for more information:  https://www.icms.org.uk/DiophantineEquationsEmergingResearchers

Another objective is 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.

Participation:

In-person attendance is by invitation only. Invited participants have been contacted directly by ICMS.

There will be an opportunity to watch the talks online via Zoom. Please note that this is a live stream only—talks will not be recorded. Details on how to obtain the Zoom link will be available here at the end of April.