Pairs of commuting integer matrices
T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen (2025).

Optimal sums of three cubes in Fq[t]
T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025).

Integral points on cubic surfaces: heuristics and numerics
T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025).

Density of rational points on some quadric bundle threefolds
D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.

Generalised quadratic forms over totally real number fields
T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912.

Square-free values of random polynomials
T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.

Strong divisibility sequences and sieve methods
T.D. Browning, M. Verzobio, Mathematika 70 (2024).

The polynomial sieve and equal sums of like polynomials
T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.

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

Uniform bounds for rational points on hyperelliptic fibrations
D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.

The Hasse principle for random Fano hypersurfaces
T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.

Free rational curves on low degree hypersurfaces and the circle method
T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.

Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5
T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.

Equidistribution and freeness on Grassmannians
T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &; Number Theory 16 (2022) 2385–2407.

Cubic Forms and the Circle Method
T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham, 2021.

Arithmetic of higher-dimensional orbifolds and a mixed Waring problem
T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.

The geometric sieve for quadrics
T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.

A geometric version of the circle method
T.D. Browning, W. Sawin, Annals of Mathematics 191 (2020) 893–948.

Density of rational points on a quadric bundle in 3×3
T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.

Free rational points on smooth hypersurfaces
T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659.