The Tenth Vasil A. Popov Prize was awarded to Matthew Colbrook, Assistant Professor at the University of Cambridge.

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 “Vasil A. Popov” Prize is presented in honour of the Bulgarian mathematician Vasil A. Popov (1942-1990), who is best known for his contribution to the Theory of Approximations.

The prize was awarded for the first time in 1995. The prize, which consists of an engraved marble statuette and a cash prize, is awarded every three years for outstanding research contributions in the field in which Vasil Popov worked. Winners of the award can be young scientists – these are individuals who have received their doctorate in the last six years.

The Tenth Vasil A. Popov Prize, which consists of a pyramid trophy and a cash award of 2000 euros, was presented to Matthew by Albert Cohen of Sorbonne Université, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee are Emmanuel Candes, Wolfgang Dahmen, Karlheinz Grochenig, Pencho Petrushev, Peter Oswald, and Vilmos Totik.