Title: **Professor of Pure Mathematics**

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CV/Bibliography (pdf)**

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 now delivers the best possible bounds for the number of variables required to deliver optimal estimates, proving the main conjecture in Vinogradov's mean value theorem. You can read about this subject here:
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** Now the subject of a European Research Council Advanced Grant -- ESTIA: Exponential Sums, Translation Invariance, and Applications**

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** Postdoctoral position(s) are currently being advertised -- see here.**

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** [Note: Bristol HR has apparently terminated an old link. If you use that old link, you will be told that the job is no longer available. The job(s) is/are VERY MUCH AVAILABLE. Use the above link to access a functional application website, and email me if you run into diffciulties.]**

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** 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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** 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, Mathematika 63 (2017), no. 1, 292--350.**

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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 2017 (2017), no. 5, 1342--1389.**

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** T. D. Wooley, Nested efficient congruencing and relatives of Vinogradov's mean value theorem,
Proc. London Math. Soc. (accepted, to appear), arxiv:1708.01220, 85pp.**

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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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** 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 JOURNAL DE THEORIE DES NOMBRES DE BOURDEAUX. 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.
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**My students:**

**Javier Pliego Garcia (PhD 20??, University of Bristol);**

**Akshat Mudgal (PhD 20??, University of Bristol);**

**Konstantinos Poulias (PhD 20??, University of Bristol);**

**Kirsti Biggs (PhD 201?, University of Bristol);**

**Bin Wei (1 year visiting PhD student from Shandong University, Jinan; now at Tianjin University);**

**Sam Chow (PhD 2016, University of Bristol; now at University of Oxford);**

**Thomas Bloom (PhD 2014, University of Bristol; now at University of Cambridge);**

**Julia Brandes (PhD 2014, University of Bristol; now at University of Gothenburg);**

**Siu Lun Alan Lee
(PhD 2013, University of Bristol);**

**Damaris Schindler (PhD 2013, University of Bristol [joint with Tim Browning]; now at Utrecht University);**

**Eugen Keil (PhD 2013, University of Bristol);**

**Sean Prendiville
(PhD 2011, University of Bristol; now at University of Manchester);**

**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!**