Posted on 21 May 2012
The grant will help Professor Velani and Professor Beresnevich establish new frameworks in number theory that could solve long-standing problems in mathematics and have potentially far-reaching benefits for the real world.
Significant progress in any of the research challenges would be a major success
Professor Sanju Velani
Spanning six years, the funding will be used to make significant contributions to topical and challenging problems in 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.
Diophantine approximation is a branch of number theory that dates back to the ancient Greeks and Chinese who used good rational approximations to the number pi (3.142...) in order to predict the position of planets and stars accurately.
Today the theory is deeply intertwined with other areas of mathematics such as ergodic theory and dynamical systems. It continues to play a significant role in applications to real-world problems including those in the rapidly developing areas of electronic communications, antenna design and signal processing. For example, advances in Diophantine approximation within the last decade have been used to investigate the potential of multiple-input and multiple-output (MIMO) technologies. These technologies have attracted attention in wireless communications for their high efficiency and reliability.
Professor David Delpy, Chief Executive of EPSRC, said: “EPSRC’s grant will help the University of York attract outstanding researchers and extend its research network, hopefully leading to enhancements in number theory. Furthermore, the wider mathematical community in the UK and beyond will also benefit since the programme will provide valuable training for early career researchers and help their professional development.”
Professor Velani said: “This programme is ambitious. Significant progress in any of the research challenges would be a major success. Six decades ago the UK became a world leader in this area. The novel nature of the proposed research will build upon the Diophantine approximation expertise in the UK and enhance the UK’s leadership in the field.”
Internationally-leading researchers at a number of institutions are active in similar or closely related research including those working at Brandeis, Minsk, Moscow, Mumbai, Princeton, Penn. State, Stanford, Strasbourg, Texas, Yale and Zurich. Many distinguished researchers plan to visit York in support of the intellectual aims of the programme. The diversity of the expertise they represent, together with the envisaged collaborations, will be crucial to its overall success.