Phone: +44 (0) 117 331 5240
E-mail: trevor.wooley@bristol.ac.uk
Address: School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, United Kingdom
Title: Professor of Pure Mathematics
Curriculum Vitae (pdf) and CV/Bibliography (pdf) Publication list: To learn about some of my more recent interests, look here or here or here.
EFFICIENT CONGRUENCING: The current hot topic for me is the new efficient congruencing approach to Vinogradov's mean value theorem, which for the first time comes within a factor of two of delivering the best possible bounds for the number of variables required to deliver optimal estimates, and comes within a whisker of proving the main conjecture. You can read about this subject here:
T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, Annals of Math. 175 (2012), 1575--1627.
T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, II, Duke Math. J. 162 (2013), 673--730.
S. T. Parsell, S. M. Prendiville and T. D. Wooley, Near-optimal mean value estimates for multidimensional Weyl sums, Geom. Funct. Anal. 23 (2013), 1962--2024.
T. D. Wooley, Translation invariance, exponential sums and Waring's problem, Proceedings of the International Congress of Mathematicians, August 13--21, 2014, Seoul, Korea, Volume II, Kyung Moon Sa Co. Ltd., Seoul, Korea, 2014, pp. 505--529.
K. Ford and T. D. Wooley, On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing, Acta Math. 213 (2014), 199--236.
T. D. Wooley, Multigrade efficient congruencing and Vinogradov's mean value theorem, Proc. London Math. Soc. (3) 111 (2015), no. 3, 519--560.
T. D. Wooley, Approximating the main conjecture in Vinogradov's mean value theorem, Mathematika (to appear), 52pp.
T. D. Wooley, The cubic case of the main conjecture in Vinogradov's mean value theorem, Adv. Math. 294 (2016), 532--561.
T. D. Wooley, Discrete Fourier restriction via efficient congruencing, Internat. Math. Res. Notices (in press), 48pp.
... and here are some consequences of EFFICIENT CONGRUENCING:
T. D. Wooley, The asymptotic formula in Waring's problem, Internat. Math. Res. Notices (2012), No. 7, 1485--1504.
T. D. Wooley, Rational solutions of pairs of diagonal equations, one cubic and one quadratic, Proc. London Math. Soc. (3) 110 (2015), no. 2, 325--356.
B. Wei and T. D. Wooley, On sums of powers of almost equal primes, Proc. London Math. Soc. (3) 111 (2015), no. 5, 1130--1162.
T. D. Wooley, Mean value estimates for odd cubic Weyl sums, Bull. London Math. Soc. 47 (2015), no. 6, 946--957.
T. D. Wooley, Perturbations of Weyl sums, Internat. Math. Res. Notices 2016 (2016), no. 9, 2632--2646.
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Now the subject of a European Research Council Advanced Grant -- ESTIA: Exponential Sums, Translation Invariance, and Applications, starting 1st September 2016
If you are interested in postdoctoral positions or PhD studentships associated with this grant, please drop me an email -- the areas of interest provide opportunities for workers in the Hardy-Littlewood circle method, arithmetic of function fields, discrete harmonic analysis, rational curves on varieties, arithmetic combinatorics and randomness extractors.
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Notes on the publication: J. Bruedern, K. Kawada and T. D. Wooley, "Additive representation in thin sequences, VIII: Diophantine inequalities in review", in: Number Theory, Dreaming in Dreams, Proceedings of the 5th China-Japan Seminar, Eds. T. Aoki, S. Kanemitsu and J. Y. Liu, World Scientific, 2009, pp. 20--79.
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Teaching: Galois Theory (updated 25 September 2016). -------------------------------------------------------------------------------Editorial work:
I'm on the Editorial Board for COMPOSITIO MATHEMATICA. If you want to submit a paper to this journal, DO NOT send the manuscript directly to me, neither by paper mail nor electronically. See here for submission instructions.
I'm on the Editorial Board for the ONLINE JOURNAL OF ANALYTIC COMBINATORICS. If you want to submit a paper to this journal, DO NOT send the manuscript directly to me, neither by paper mail nor electronically. See here for submission instructions.
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Journal prices and a quick opinion on open-access journals -------------------------------------------------------------------------------Slides of Bristol Colloquium (19/11/2007): Waring's problem, the declining exchange rate between small powers, and the story of 13,792.
My students:
Kirsti Biggs (PhD 201?, University of Bristol);
Bin Wei (1 year visiting PhD student from Shandong University, Jinan);
Sam Chow (PhD 2016, University of Bristol);
Thomas Bloom (PhD 2014, University of Bristol; now at University of Bristol);
Julia Brandes (PhD 2014, University of Bristol; now at Universitaet Goeteborg);
Siu Lun Alan Lee (PhD 2013, University of Bristol);
Damaris Schindler (PhD 2013, University of Bristol [joint with Tim Browning]; now at IAS, Princeton);
Eugen Keil (PhD 2013, University of Bristol);
Sean Prendiville (PhD 2011, University of Bristol; now at University of Oxford);
Craig Spencer (PhD 2008, University of Michigan; now at Kansas State University);
Matthew Smith (PhD 2007, University of Michigan; now at Berklee College of Music);
Mike Knapp (PhD 2000, University of Michigan; now at Loyola College);
Scott Parsell (PhD 1999, University of Michigan; now at West Chester University);
Eric Freeman (PhD 1999, University of Michigan; now at University of California, Berkeley;)
Joel Wisdom (PhD 1998, University of Michigan; now at U.S. Government)
Greg Martin (PhD 1997, University of Michigan [joint with Hugh Montgomery], now at University of British Columbia)
Morley Davidson (PhD 1995, University of Michigan; now at Kent State University, Ohio) NEWS ITEM!
