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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.

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work+44 (0)117 331 8092
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Qualifications MA(Cantab), PhD(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.