Title: **Professor of Pure Mathematics**

**Curriculum Vitae or (pdf) Curriculum Vitae (not really fully up to date)
Publication list:
To learn about some of my more recent interests, look here or
here or here.**

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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:
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** T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, Annals of Math. 175 (2012), 1575--1627.**

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** T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, II, Duke Math. J. 162 (2013), 673--730.**

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** 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.**

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** 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.**

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** K. Ford and T. D. Wooley, On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing, Acta Math. 213 (2014), 199--236.**

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** T. D. Wooley, Multigrade efficient congruencing and Vinogradov's mean value theorem, Proc. London Math. Soc. (3) 111 (2015), no. 3, 519--560.**

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** T. D. Wooley, Approximating the main conjecture in Vinogradov's mean value theorem, submitted, 52pp.**

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** T. D. Wooley, The cubic case of the main conjecture in Vinogradov's mean value theorem, Adv. Math. 294 (2016), 532--561.**

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** T. D. Wooley, Discrete Fourier restriction via efficient congruencing, Internat. Math. Res. Notices (in press), 48pp.**

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... and here are some consequences of EFFICIENT CONGRUENCING:
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** T. D. Wooley, The asymptotic formula in Waring's problem, Internat. Math. Res. Notices (2012), No. 7, 1485--1504.**

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** 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.**

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** 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.**

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** T. D. Wooley, Mean value estimates for odd cubic Weyl sums, Bull. London Math. Soc. 47 (2015), no. 6, 946--957.**

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** 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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**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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**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 201?, 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!**