[5] He was a von Kármán instructor at California Institute of Technology from 2008 to 2009, held a junior research fellowship at Homerton College, Cambridge from 2009 to 2012, and held a Marie Skłodowska-Curie Actions fellowship at the University of Vienna in 2012.

[6] Among other results, he has established the Solvability Complexity Index (SCI) and its following classification hierarchy.

[7][8][9][10][11] It is linked [8] to Steve Smale's question [12] on the existence of iterative convergent algorithms for polynomial root finding answered by Curt McMullen[13][14] and Peter Doyle,[14] as well as Alan Turing's work and the Arithmetical hierarchy.

In 2017, he was awarded the Leverhulme Prize for having "solved very hard problems and opened new directions in areas of great impact in applied analysis [...] Notably, by introducing the Solvability Complexity Index he has made a major contribution to the advancement of Smale’s programme on the foundation of computational mathematics".

[18] In 2019, he was awarded the Whitehead Prize of the London Mathematical Society for having "contributed fundamentally to the mathematics of data, sampling theory, computational harmonic analysis and compressed sensing" and "especially his development of the Solvability Complexity Index and its corresponding classification hierarchy ".