[1] Boucksom studied at the École normale supérieure de Lyon from 1996 to 1999, when he qualified with his agrégation in mathematics.
He received his doctorate in 2002 from the Institut Fourier of the Université Grenoble Alpes with thesis Cônes positifs des variétés complexes compactes under the supervision of Jean-Pierre Demailly.
[2] As a postdoc Boucksom studied with Simon Donaldson at Imperial College London.
The laudation cited his work on positive fluxes in compact Kähler manifolds with application to characterization of pseudo-effective cones,[5] as well as his work on the Monge-Ampère equation with application to the existence of Kähler-Einstein metrics with minimal singularities.
In 2018 Boucksom was an Invited Speaker with talk Variational and non-Archimedean aspects of the Yau-Tian-Donaldson conjecture at the International Congress of Mathematicians in Rio de Janeiro.