Department of Mathematics, University of Bristol
University Walk, Clifton
44 (117) 3315240
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- BA Hons Mathematics-University of Cambridge (1987)
- CASM (Part III)-University of Cambridge (1988)
- PhD Pure Mathematics-Imperial College of Science and Technology, University of London (1990)
Trevor Wooley 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 His 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.