“It continues to play a significant role in applications to real-world problems including those in electronic communications, antenna design and signal processing,” said the Engineering and Physical Sciences Research Council (EPSRC), which is providing the £1.6m grant over six years.
Professor Sanju Velani and Professor Victor Beresnevich will lead the work, aiming to establish frameworks in number theory that could solve long-standing problems in mathematics with potential real-world benefits.
“EPSRC’s grant will help the University of York attract outstanding researchers and extend its research network, hopefully leading to enhancements in number theory,” said EPSRC CEO Professor David Delpy. “Furthermore, the wider mathematical community in the UK and beyond will also benefit since the programme will provide training for early career researchers and help their professional development.”
The aim is to make “significant”, said EPSRC, contributions to the theory of Diophantine approximation, in particular to Littlewood’s Conjecture, the Duffin-Schaeffer Conjecture and the generalised Baker-Schmidt problem.
“In the past, these three problems were thought to be unrelated. However recent advances have shown that there are substantial links, meaning that progress in one problem will have impact on others. Exploiting the links is a key feature of the programme,” said the research Council.
Diophantine approximation is a branch of number theory that dates back to the ancient Greeks and Chinese who used good rational approximations (like 22/7) to the pi in order to predict the position of planets and stars.
“Today the theory is deeply intertwined with other areas of mathematics such as ergodic theory and dynamical systems,” said EPSRC.
“This programme is ambitious. Significant progress in any of the research challenges would be a major success,” said Velani. “Six decades ago the UK became a world leader in this area. “The novel nature of the proposed research will build upon this expertise and enhance the UK’s leadership.”