Professor Laleg-Kirati's research interests encompass work across the fields of applied mathematics, control systems, and signal analysis. She works on new methods for signal analysis based on a semi-classical approach with an application to the analysis of the arterial blood pressure. Laleg-Kirati is also interested in modeling, identification, control, fault detection, inverse problems and especially seismic inversion and has expertise in solitons waves and scattering theory.