Directory of Experts
Details for Professor Trevor Wooley
| Personal details | |
| Name | Professor Trevor Wooley |
| Job title | Professor of Pure Mathematics |
| Department | School of Mathematics University of Bristol |
| Contact details | This expert can be contacted via the University of Bristol Public Relations
Office. To help us deal with your request, please mention the Directory of Experts when contacting the Public Relations Office. work+44 (0)117 331 8092 email: public-relations@bristol.ac.uk |
| Qualifications | M.A.(Cantab.), Ph.D.(Lond.) |
| Professional details | |
| Membership of professional bodies | London Mathematical Society European Mathematical Society American Mathematical Society |
| Keywords | Hardy-Littlewood method Diophantine equations arithmetic geometry arithmetic harmonic analysis exponential sums Waring's problem analytic number theory |
| Areas of expertise | My research is centred on the Hardy-Littlewood (circle) method, a method based on the use of Fourier series that delivers asymptotic formulae for counting functions associated with arithmetic problems. In the 21st Century, this method has become immersed in a turbulent mix of ideas on the interface of Diophantine equations and inequalities, arithmetic geometry, harmonic analysis and ergodic theory, and arithmetic combinatorics. Perhaps the most appropriate brief summary is therefore "arithmetic harmonic analysis". Much of my work hitherto has focused on Waring's problem (representing positive integers as sums of powers of positive integers), and on the proof of local-to-global principles for systems of diagonal diophantine equations and beyond. More recently, we have explored the consequences for the circle method of Gowers' higher uniformity norms, the use of arithmetic descent, and function field variants. The ideas underlying each of these new frontiers seem to offer viable approaches to tackling Diophantine problems known to violate the Hasse principle. |