The Tenth Vasil A. Popov Prize was awarded to Matthew Colbrook

The Tenth Vasil A. Popov Prize was awarded to Matthew
Colbrook, on June 19, 2023 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 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.
https://www.ljll.math.upmc.fr/popov-prize/