Boutin's research is in the area of applied mathematics, signal processing and machine learning. Mathematically speaking, she is interested in discrete inverse problems. The methods she uses include Lie groups, invariant theory, commutative algebra, and PDEs, among others. One of the particularities of her work is that it often integrates geometric tools inside a probabilistic framework. In particular, she has worked on building lossless representations of objects using invariant statistics., including different unlabeled distance geometry problems.

Originally from Québec, Boutin obtained a Ph.D. in Mathematics under the supervision of Peter Olver at the University of Minnesota. She held postdoctoral positions at Brown University in Rhodes Island and at the Max Planck Institute for Mathematics in the Sciences in Leipzig. She was on the faculty of Purdue University in West Lafayette for several years before joining TU/e.