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

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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.AP2026

A sharp isoperimetric inequality for the Neumann--Poincaré operator in every dimension

Matthew J. Colbrook, Siavash Sadeghi

Let $Ω \subset R^{d}$ , $d \geq 2$ , be a bounded connected domain with boundary of class $C^{1, α}$ , where $0 < α < 1$ . For the adjoint Neumann--Poincaré operator $K_{\partial Ω}^{*}$ , no…

math.AP2026

A computer-assisted counterexample to the planar Berenstein conjecture

Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants

Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial,…

math.AP2026

A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures

Matthew J. Colbrook, George Stepaniants

The planar Pompeiu problem, originating in 1929, and the associated Schiffer conjecture are long-standing rigidity questions linking rigid-motion integral transforms and Fourier ze…