| Project Detail |
Geometry and number theory are core disciplines within pure mathematics, with many repercussions across science and society. They are subjects that have attracted some of the best minds in mathematics since the time of the Ancient Greeks and continue to exert a natural fascination on professional and amateur mathematicians alike. Throughout the history of mathematics, both topics have often inspired major mathematical developments which have had enormous impact beyond their original applications. The fascination of number theory is exemplified by the story of Fermats last theorem, the statement of which was written down in 1637 and which is simple enough to be understood by anyone familiar with high school mathematics. It took more than 350 years of hard work and significant developments across mathematics before Wiless celebrated proof was finally published in 1995. Wiless proof, for which he was awarded the prestigious Abel Prize in 2016, involves a mixture of ideas from number theory and geometry, and the interplay between these topics is one of the
most active areas of research in pure mathematics today.
For example, the work of Ngo on the Langlands program (for which he was awarded the Fields Medal in 2010, the highest honour in mathematics) and Scholze on arithmetic algebraic geometry (for which he was offered a New Horizons in Mathematics Breakthrough Prize in 2016, and is expected to be awarded the Field Medals this year), show the significant impact of geometric ideas on number theory. In the other direction, number theory has been used to prove conjectures in geometry, including a path proposed by Kontsevich (Fields Medal 1998, Breakthrough Prize 2015) and Soibelman to help solve one of the major open problems in geometry, the SYZ conjecture, which lies at the interface of geometry and theoretical physics. These and other connections between geometry and number theory continue to lead to some of the most exciting research developments in mathematics.
This CDT will be run by a partnership of researchers at Imperial College London, Kings College London, and University College London, which together form the largest and one of the strongest UK centres for geometry and number theory.
By training mathematicians to PhD level in geometry and number theory, and by ensuring that more general skills (for example, computing, communication, teamwork, leadership) are embedded as a demanding and enjoyable part of our programme, this CDT will deliver the next generation of highly trained researchers able to contribute not only to the UKs future educational needs but also to those of the financial and other high-tech industries. Our graduates will contribute directly to national security (GCHQ is, for example, a user of high-end pure mathematics) but also more indirectly as employees in industries which value the creative and novel approach that mathematicians typically bring to problem solving. |
