Tim Browning

collaborators

3 papers

math.NT2026

Beyond the square-root barrier: cubic forms of Perazzo type

Tim Browning, Ritabrata Munshi, Victor Y. Wang

We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.

math.NT2025

Random Diophantine equations of large degree

Tim Browning, Will Sawin

Among the set of hypersurfaces of degree $d$ and dimension $ℓ$ defined by the vanishing of a homogeneous polynomial with coefficients $\pm 1$ , we investigate the probability tha…

math.NT2025

Pairs of commuting integer matrices

Tim Browning, Will Sawin, Victor Y. Wang

We prove upper and lower bounds on the number of pairs of commuting $n \times n$ matrices with integer entries in $[- T, T]$ , as $T \to \infty$ . Our work uses Fourier analysis and lead…