Mezić's research is centered around operator-theoretic approach to analysis of nonlinear dynamical systems, applications in microfluidics and (bio)-nanotechnology. The research topics can be grouped as follows:- Mixing and separation in fluids across the scales with applications ranging frommicrofluidic phenomena to oceanographic flows.- Nano and micro-scale particle dynamics induced by dielectrophoresis and otherelectrokinetic phenomena, with applications to biotechnology.- Multiscale dynamics of the Atomic Force Microscope, including interactions with biomolecules.- Dynamical systems theory of complex systems, including large-scale networked systems.In each of these topics, the research is characterized by pursuit of the key physical phenomena in a device or system followed by the abstraction of the mathematical problem (or problems) associated with it. We close the loop by applying the solution of the mathematical problem to explain the physical phenomena or design new concepts based on which devices can be built or improved.