Matthew J. Colbrook

activity

20162026

most citedCan stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem

130 citations · 345 across the 38 of their papers we have counts for

collaborators

47 papers

math.NA2026

Computing Spectral Properties of Differential Operators on Surfaces

Gustav Conradie, Matthew J. Colbrook, Daniel Fortunato

Computing spectra of differential operators on surfaces is crucial in many applications, ranging from medical image analysis to nanoscale quantum structures. However, discretizatio…

math.CO2026

Crown graphs maximise the representation number of bipartite graphs

Matthew J. Colbrook, Catherine Drysdale

The representation number of a graph is the least positive integer $k$ for which its vertices can be arranged in a word, each occurring $k$ times, so that two distinct letters alte…

math.AP2026

A counterexample to Kenig's conjecture for the Laplace double-layer operator

Matthew J. Colbrook, Siavash Sadeghi

We disprove Kenig's 1994 spectral-radius conjecture for the double-layer operator in every dimension $d \geq 2$ . For every $t > 1/2$ sufficiently close to $1/2$ , we construct a bounded…

math.NA2026

A Complete Resolution of Forsythe's Conjecture for Restarted Conjugate Gradients

Matthew J. Colbrook, George Stepaniants, Alex Townsend

Forsythe's conjecture, published in 1968, asserts that for each restart length $s$ , every exact-arithmetic restarted conjugate-gradient iteration on a real symmetric positive defin…

math.SP2026

Finiteness and exponential growth of full graph $p$ -spectra

Matthew J. Colbrook

We prove that the full spectrum of the graph $p$ -Laplacian is finite for every finite graph and every real $p > 1$ . This resolves the problem of finiteness of the full graph spectrum…