# Popov Prize 2023 Winner

### 2023 - Tenth Prize Recipient

# Matthew Colbrook

The Tenth Vasil A. Popov Prize was awarded on June 19, 2023 to Matthew Colbrook from the University of Cambridge at the 2023 Foundations of Computational Mathematics (FoCM) conference.

Matthew (Matt) was recognized for his outstanding contributions to approximation theory, particularly his work on the approximation of spectral properties of operators in infinite-dimensional spaces and the approximation power and trainability of neural networks. Computing approximations of spectra in infinite dimensions has been a significant challenge for mathematicians since the 1950s. Matt has introduced new algorithms that converge and come with explicit approximation guarantees. He has also developed a myriad of techniques yielding optimal approximation results for different spectral properties of operators, classifying when this can and cannot be done in the Solvability Complexity Index Hierarchy, and solving other open problems such as approximating generic spectral measures, geometric spectra, and (data-driven) Koopman operators in dynamical systems. Parallel to this work, Matt has contributed significantly to the problem of approximation power and trainability of neural networks. For example, in a paper published in Proceedings of the National Academy of Sciences (PNAS), Matt and his collaborators have shown that there are problems where stable and accurate neural networks exist, yet no training algorithm can produce such a network.

The Prize, which consists of an engraved pyramid trophy and a cash award of 2000 euros, was presented to Matt by Albert Cohen of Sorbonne UniversitĂ©, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee were Emmanuel Candes, Wolfgang Dahmen, Karlheinz Grochenig, Pencho Petrushev, Peter Oswald, and Vilmos Totik.

Matt is an Assistant Professor at the University of Cambridge. He received his PhD in September 2020 from the University of Cambridge under the supervision of Anders C. Hansen.