## Breadcrumb

### Prof Trevor Wooley

Office: 4.18 Howard House

Department of Mathematics

University Walk, Clifton, Bristol BS8 1TW, U.K.

Telephone:
+44 (0)117 331-5240

Extension: 15240

Mail: trevor.wooley

http://www.maths.bris.ac.uk/~matdw

#### Education

- 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)

#### Honours

- Fellow of the Royal Society (2007)
- Royal Society Wolfson Research Merit Award (2007 - 2012)
- 45-minute Invited Speaker, International Congress of Mathematicians, Beijing (2002)
- Salem Prize (1998)
- Junior Berwick Prize of the London Mathematical Society (1993)
- David and Lucile Packard Fellow (1993 - 1998)
- Alfred P. Sloan Research Fellow (1993 - 1995)

#### Publications

**Vinogradov's mean value theorem via efficient congruencing** (2012)

Trevor D. Wooley

Annals of Mathematics vol: 175 , Issue: 3 , Pages: 1575 - 1627

*URL provided by the author*

**Near-optimal mean value estimates for multidimensional Weyl sums** (2013)

S. T. Parsell, S. M. Prendiville and T. D. Wooley

Geom. Funct. Anal. vol: 23 , Issue: 6 , Pages: 1962 - 2024

*URL provided by the author*

#### Research Interests

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.