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Browning Group

Analytic Number Theory and Its Interfaces

What is the precise connection between adding and multiplying whole numbers? This is a surprisingly deep question that can be thought about in many different lights. One natural extension studies the sequence of integers that arise as solutions to a polynomial equation with integer coefficients, viz. a Diophantine equation. The Browning group works on understanding such sequences using a blend of analytic, geometric and algebraic methods.

Low-dimensional Diophantine equations have been heavily exploited in cryptography, but the properties of higher-dimensional Diophantine equations remain largely mysterious. Hilbert’s 10th problem asks for an algorithm to decide if a given Diophantine equation has integer solutions or not. Methods of mathematical logic have revealed this to be an impossible dream, but we would still like to know if such a procedure exists when we merely ask for solutions in rational numbers. Moreover, when solutions are known to exist, there are deep conjectures that connect their spacing to the intrinsic geometry of the equation. In recent years quantitative methods have been found to be remarkably effective at resolving these fundamental questions. The Browning group is involved in actively expanding the available toolkit for studying these problems and their generalizations.


Current Projects

Moduli spaces of rational curves | Rational points on Fano varieties | Arithmetic statistics | Hardy-Littlewood circle method | Sieve theory and divisibility sequences


Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. View

Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240. View

Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. View

Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics over a split quadric surface. Involve. 16(2), 331–342. View

Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203. View

View All Publications

ReX-Link: Timothy Browning


Since 2018 Professor, Institute of Science and Technology Austria (ISTA)
2012 – 2019 Professor, University of Bristol, UK
2008 – 2012 Reader, University of Bristol, UK
2005 – 2008 Lecturer, University of Bristol, UK
2002 – 2005 Postdoctoral Research Fellow, University of Oxford, UK
2001 – 2002 Postdoctoral Research Fellow, Université de Paris-Sud, Orsay, France
2002 PhD, Magdalen College, University of Oxford, UK

Selected Distinctions

2022 Member of Academia Europaea
2021 Ferran Sunyer i Balaguer Prize
2017 Simons Visiting Professorship (MSRI)
2012 ERC Starting Grant
2010 Phillip Leverhulme Prize
2009 Ferran Sunyer i Balaguer Prize
2008 Whitehead Prize

Additional Information

Download CV
Open Browning website
Browning Group Working Seminar
Algebraic Geometry & Number Theory Seminar
Mathematics at ISTA

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