Personal details 
Name 
Professor Trevor
Wooley 
Job title 
Professor of Pure Mathematics

Department 
School of Mathematics University of Bristol

Contact details 
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work+44 (0)117 331 8092
email: publicrelations@bristol.ac.uk

Qualifications 
MA(Cantab), PhD(Lond) 
Professional details 
Membership of professional bodies 
London Mathematical Society European Mathematical Society American Mathematical Society

Keywords 
HardyLittlewood 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 HardyLittlewood (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 localtoglobal 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.
