Dr. Panagiotou's research spans pure, applied and computational mathematics.

In particular, she is interested in the effects of topological entanglement in physical systems, such as polymers. The study of topological entanglement in polymers involves topology and geometry to create new topological/geometrical tools for such systems and computational methods that allow for their application to physical systems. To study polymer material properties, she uses Molecular Dynamics Simulations and Field-Theoretic Simulations.