His research interests revolve around geometry, and particularly, the study of discrete geometry. This vast area includes animation and simulation of 3D objects, processing of polygonal meshes (compression, curvature analysis, remeshing, etc), haptics, as well as more theoretical work on the foundation of computations on discrete manifolds (Discrete Exterior Calculus). Mathieu received the NSF Young Investigator Award in 2001 and the SIGGRAPH Significant New Researcher Award in 2003.