At Pierre and Marie Curie University (Paris 6) he graduated in 1996 with Thèse de Doctorat (PhD) under the supervision of Thierry Cazenave.
Martel's research deals with partial differential equations from mathematical physics, especially solitons.
Martel was a Maître de conférences at Cergy-Pontoise University from 1997 to 2004, on leave at École Polytechnique as a full-time associate professor (Professeur chargé de cours à temps complet) from 2002 to 2004.
[2] In 2008 Martel was an invited speaker at the European Congress of Mathematics in Amsterdam.
[3] In 2018 he was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro.