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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, TD & Loughran, D, 2017, ‘Varieties with too many rational points’.
*Mathematische Zeitschrift*, vol 285., pp. 1249?1267 - Browning, T & Schindler, D, 2017, ‘Strong approximation and a conjecture of Harpaz and Wittenberg’.
*International Mathematics Research Notices*. - 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, 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 & Gorodnik, A, 2017, ‘Power-free values of polynomials on symmetric varieties’.
*Proceedings of the London Mathematical Society*. - Browning, T, 2017, ‘Many cubic surfaces contain rational points’.
*Mathematika*. - Browning, TD & Vishe, P, 2017, ‘Rational curves on smooth hypersurfaces of low degree’.
*Algebra and Number Theory*. - 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 - Browning, T & Vinogradov, I, 2016, ‘Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1’.
*Journal of the London Mathematical Society*, vol 83., pp. 563-584 - Browning, TD & Matthiesen, L, 2016, ‘Norm forms for arbitrary number fields as products of linear polynomials’.
*Annales Scientifiques de l'École Normale Supérieure*.

View complete publications list in the University of Bristol publications system

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