Mathematicians at the Universities of Nottingham and Oxford have won one of the largest ever pure maths research grants awarded in the EU — £2.3m to work on solutions of some of the most famous unsolved maths problems.
The Millennium problems are seven mathematical questions which were chosen by a committee of world-leading mathematicians and proposed by the Clay Mathematics Institute in the United States in the year 2000. One problem was solved in 2004 but the remaining six are still testing mathematical brains all over the world today.
Now, thanks to funding from the Engineering and Physical Sciences Research Council (EPSRC), Ivan Fesenko, Professor of Pure Mathematics at The University of Nottingham, will lead a team of ‘big names’ in the field to intensify efforts to solve some of the questions. They will work in a radically new intra-disciplinary way towards the greatest challenges in modern mathematics.
Professor Fesenko told John Humphrys on Radio 4's Today programme: "If you think about modern mathematics it is like a very large old oak tree, with many, many branches still developing. Most mathematicians are working and sitting on one of those new branches. By taking into account at least seven of these larger branches hopefully we will better understand some of those famous problems."
These immense challenges have proved to be impenetrable for direct attacks of individual mathematicians. This undoubtedly requires a change in the way that mathematicians usually work.
The team will work on two of the Problems, the generalized Riemann Hypothesis and the conjecture of Birch and Swinnerton-Dyer. The research will tackle higher developments in the Langlands Programme which is viewed as a grand unification theory in all of mathematics. This Programme is a network that interconnects many areas of mathematics and physics including electro-magnetic duality and conformal field theory.
The highly popular bestselling book ‘Love & Math’ by E. Frenkel, a mathematician from Berkeley and a senior visitor on the grant, explains many of its key features.
Ivan explains: “Among the many sensibilities that humans have, two are very basic: the sensibility of the discrete, and the sensibility of the continuous. The sensibility of the discrete forms the basis of counting and hence of economics, that of the continuous forms the basis of drawing, one of the arts.
“These two basic ways of apprehending the sensible have led to the development of arithmetic and of geometry respectively by means of finding formal languages to express them. Many fundamental changes in mathematics have arisen from insights into how one sensibility could be understood in terms of the other. From internet pages and enormously successful internet-based start-ups to the pictorial presentation of quantum mechanical algorithms, the effectiveness of geometric cognition is seen all around us.
“Numbers are the most basic object of mathematics. Yet, the most hard and unsolved problems in mathematics are about numbers. The simplicity of their definition hides an underlying immense complexity and profound depth. Despite many previous great achievements, we are still missing a powerful geometric view of numbers that will reveal and apply their underlying continuous nature as opposed to their discrete appearance.”
Using the features of EPSRC programme grants, the Nottingham-Oxford team will develop new fundamental insights and approaches to several key types of geometries, including very recent ones, and create many links between them.
The research is designed to develop new tools and theories for mathematicians working in geometry, arithmetic geometry, algebra, model theory and mathematical physics.
The team includes I. Fesenko (Nottingham, Principal Investigator), F. Bogomolov (Nottingham/Courant Inst.), N. Hitchin (Oxford), M. Kim (Oxford), K. Kremnitzer (Oxford), B. Zilber (Oxford). The range of areas of the team members varies from geometry to logic to number theory.
More detail on the Millennium Problems of the Clay Mathematics Institute are available here.
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Notes to editors: The University of Nottingham has 43,000 students and is ‘the nearest Britain has to a truly global university, with campuses in China and Malaysia modelled on a headquarters that is among the most attractive in Britain’ (Times Good University Guide 2014). It is also one of the most popular universities in the UK among graduate employers, in the top 10 for student experience according to the Times Higher Education and winner of ‘Research Project of the Year’ at the THE Awards 2014. It is ranked in the world’s top one per cent of universities by the QS World University Rankings, and 8th in the UK by research power according to REF 2014.
The University of Nottingham in Malaysia (UNMC) is holding events throughout 2015 to celebrate 15 years as a pioneer of transnational education. Based in Semenyih, UMNC was established as the UK's first overseas campus in Malaysia and one of the first world-wide.
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