Gallagher is a professor at École Normale Supérieure in Paris and the Université de Paris, and member of the CNRS laboratory DMA (Département de Mathématiques et Applications). She is a former student of the École Polytechnique, holder of a Ph.D. from Sorbonne Université (formerly UPMC), and a former CNRS research fellow at the Université Paris Sud and the Ecole Polytechnique.
Gallagher is a specialist in non-linear partial differential equations, particularly mechanics equations. She and her collaborators have made good progress on Hilbert’s sixth problem, seeking to reconcile microscopic and macroscopic descriptions of fluids. Her work has been awarded many times. In particular, she received the 2008 Paul Doistau-Émile Blutet Prize and the 2018 Sophie Germain Prize from the Académie des Sciences and the CNRS silver medal in 2016.