Strategic package (for Professor Sir Andrew Wiles FRS)
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
Professor Sir Andrew Wiles FRS, who famously proved Fermat's Last Theorem, is probably the most celebrated mathematician in the world. He is currently engaged in research on the Birch Swinnerton-Dyer conjecture and special values of L-functions, a field in which there is much active research, both in the UK and world-wide. Needless to say, any real progress on the Birch Swinnerton-Dyer conjecture would be a spectacular achievement. Wiles already has an important early result, with Coates, in this area. The conjecture is wide open for elliptic curves of rank two or more, and Wiles, together with two postdoctoral researchers, plans to explore this problem in great detail.
Organisations
People |
ORCID iD |
| Sam Howison (Principal Investigator) |
Publications
Andrade J
(2015)
A simple proof of the mean value of | K 2 ( O ) | in function fields
in Comptes Rendus Mathematique
Andrade J
(2016)
Mean values of derivatives of L-functions in function fields: I
in Journal of Mathematical Analysis and Applications
Andrade J
(2016)
Rudnick and Soundararajan's theorem for function fields
in Finite Fields and Their Applications
Andrade J
(2016)
Average values of L-series for real characters in function fields
in Research in the Mathematical Sciences
Andrade JC
(2015)
Shifted convolution and the Titchmarsh divisor problem over q[t].
in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Ardakov K
(2016)
A canonical dimension estimate for non-split semisimple -adic Lie groups
in Representation Theory of the American Mathematical Society
Browning T
(2017)
Forms in many variables and differing degrees
in Journal of the European Mathematical Society
Browning T
(2014)
RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES
in Journal of the Institute of Mathematics of Jussieu
Bui H
(2013)
On simple zeros of the Riemann zeta-function
in Bulletin of the London Mathematical Society
| Description | Amongst the most interesting findings are Andrew Wiles' work on quadrartic class numbers, where he demonstrates the existence of imaginry quadratic fields of class number coprime to a given prime, and with prescribed splitting properties at a finite number of places. Also worthy of special note are Julio Andrade's many papers on arithmetic over function fields. Further developments of this are in the pipeline and/or still being refereed. Among Heath-Brown's papers a key finding is that one can establish the infinitude of primes of the shape a^2+p^4, where p is itself prime. |
| Exploitation Route | The results are of great interest to other academic researchers in Number Theory and, as is often the case for pure mathematics, may have unforeseen practical uses many years from now. |
| Sectors | Digital/Communication/Information Technologies (including Software),Security and Diplomacy |
| Description | Number Theory workshops |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Undergraduate students |
| Results and Impact | The package supported a series of workshops in Number Theory for students from across the UK who learned about contemporary challenges in the subject. |
| Year(s) Of Engagement Activity | 2013,2014,2015 |
| Description | Public lectures |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Schools |
| Results and Impact | Andrew Wiles has given several 'engagement' lectures on his work, very successfully taking the audience from elementary considerations of quadratic equations right through to his own contributions, both in proving Fermat's Conjecture and on the Birch--Swinnerton-Dyer conjecture. The lectures were extremely well attended with high numbers of young people from local schools. (There was also a similarly successful talk to Oxford alumni.) |
| Year(s) Of Engagement Activity | 2011,2014 |