Conference: Diophantine Equations, Combinatorics, and Analysis in Number Theory

The International Centre for Mathematical Sciences in Edinburgh, United Kingdom will host the workshop Diophantine Equations, Combinatorics, Analysis in Number Theory on June 23-27, 2025, and a related two-day conference aimed at early-career researchers, Diophantine Equations, Combinatorics, Analysis in Number Theory: Emerging Researchers, will be held June 19-20. This grant will support participation in these programs by early-career researchers from the United States, which will enhance the U.S. pipeline of mathematical talent by providing a unique opportunity for networking and collaboration. This event will be the first of its kind to bring together researchers in Diophantine equations, arithmetic combinatorics, and harmonic analysis. Recent breakthroughs surrounding Vinogradov's Mean Value Theorem and three-term arithmetic progressions have led to significant progress in these areas. Moreover, the associated techniques are frequently intertwined and generate unexpected insights when applied to problems that may at first seem unrelated. A striking example is the relationship between decoupling in harmonic analysis and efficient congruencing in number theory. Connecting experts from these cognate fields in a workshop-style environment will foster cross-disciplinary collaborations and lead to seminal research papers. https://www.icms.org.uk/DiophantineEquations https://www.icms.org.uk/DiophantineEquationsEmergingResearchers This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.