Roy works in real algebraic geometry in particular real spectra and, most recently, in complexity of algorithms in real algebraic geometry and also the applications.[2]
In 1986, Roy was one of the founders[6] of European Women in Mathematics (EWM), and was the convenor (president) of EWM 2009–2013.[7] In 1987 she co-founded the French organization for women in mathematics, Femmes et Mathématiques, and became the organization's first president.
Roy is scientific officer for Sub-Saharan Africa in Centre International de Mathématiques Pures et Appliquées, CIMPA].[8] Roy is president of Association d'Echanges Culturels Cesson Dankassari (Tarbiyya-Tatali) an organization working for joint activities in a commune Dan-Cassari in Niger and the French commune Cesson-Sévigné.
with Jacek Bochnak, Michel Coste: Real algebraic geometry. 2.Edition, Springer, Ergebnisse der Mathematik Bd. 36, 1998 (first in French 1. Edition 1987).
Three Problems in real algebraic geometry and their descendants. In: Engquist, Schmid: Mathematics unlimited- 2001 and beyond. Springer Verlag 2000, S. 991 (Hilberts 17th Problem, Algorithms, Topology of real algebraic varieties).
Géométrie algébrique réelle. In: Jean-Paul Pier (Hrsg.): Development of Mathematics 1950-2000. Birkhäuser 2000.
Introduction a la geometrie algebrique reelle, Cahiers Sem. Hist. Math., 1991, Online