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# Professor Tim Browning

## Professor Tim Browning

MSci(Lond), DPhil(Oxon)

Professor in Number Theory
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MSci(Lond), DPhil(Oxon)

Office Room 5.16

Howard House,

Queen's Ave,
Bristol
BS8 1SN

(See a map)

+44 (0) 1173315242

t.d.browning@bristol.ac.uk

I am a number theorist working at the interface of analytic number theory and Diophantine geometry, interested in questions about rational points on algebraic varieties over non-closed fields.

**PhD projects**

I am interested in all aspects of analytic number theory, with a special emphasis on problems that lie at the interface with Diophantine geometry. My research in this area involves developing analytic tools (such as sieve methods or the Hardy-Littlewood circle method) to study the density (or existence) of rational (or integral) points on algebraic varieties. My interests would suit anyone looking to work in analytic number theory, broadly interpreted, or anyone interested in combining tools from analytic number theory with concepts from algebraic geometry. I am happy to discuss further details of possible projects in this area by email, some indication of which can also be found on my web page.

- analytic number theory
- rational points

- Browning, T & Loughran, D, 2018, ‘Sieving rational points on varieties’.
*Trans. Amer. Math. Soc*. - Browning, T & Schindler, D, 2017, ‘Strong Approximation and a Conjecture of Harpaz and Wittenberg’.
*International Mathematics Research Notices*. - Browning, T, 2017, ‘Many cubic surfaces contain rational points’.
*Mathematika*, vol 63. - Browning, T & Heath-Brown, R, 2017, ‘Forms in many variables and differing degrees’.
*Journal of the European Mathematical Society*, vol 19., pp. 357-394 - Browning, TD & Matthiesen, L, 2017, ‘Norm forms for arbitrary number fields as products of linear polynomials’.
*Annales Scientifiques de l'École Normale Supérieure*, vol 50., pp. 1375-1438 - Browning, TD & Vishe, P, 2017, ‘Rational curves on smooth hypersurfaces of low degree’.
*Algebra and Number Theory*, vol 11., pp. 1657?1675 - Browning, TD & Loughran, D, 2017, ‘Varieties with too many rational points’.
*Mathematische Zeitschrift*, vol 285., pp. 1249?1267 - Browning, TD & Prendiville, SM, 2017, ‘Improvements in Birch's theorem on forms in many variables’.
*Journal für die reine und angewandte Mathematik*, vol 2017., pp. 203-234 - Browning, TD & Gorodnik, A, 2017, ‘Power-free values of polynomials on symmetric varieties’.
*Proceedings of the London Mathematical Society*. - Browning, TD & Prendiville, SM, 2017, ‘A Transference Approach to a Roth-Type Theorem in the Squares’.
*International Mathematics Research Notices*, vol 2017., pp. 2219-2248

View complete publications list in the University of Bristol publications system

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