Toomre's research and teaching centers on astrophysical fluid dynamics (AFD), with particular emphasis on nonlinear theories for compressible convection in stars, and in studying nonlinear dynamical systems exhibiting multiple bifurcations and chaos. He is particularly interested in topics where theoretical work related to fluid dynamics can be challenged and tested by observation and experiment. He is active in turbulence theory and simulation, with extensive experience in the use of vector supercomputers, massively parallel machines, high-speed networks, archival storage systems, and major visualization systems. Toomre's teaching spans graduate courses in basic fluid dynamics, waves and instabilities, nonlinear dynamical systems, geophysical and astrophysical fluid turbulence, magnetohydrodynamics, mathematical methods, computational mathematics and simulations, and a variety of courses in general astronomy.
The Physics Frontiers Centers (PFC) program supports university-based centers and institutes where the collective efforts of a larger group of individuals can enable transformational advances in the most promising research areas. The program is designed to foster major breakthroughs at the intellectual frontiers of physics by providing needed resources such as combinations of talents, skills, disciplines, and/or specialized infrastructure, not usually available to individual investigators or small groups, in an environment in which the collective efforts of the larger group can be shown to be seminal to promoting significant progress in the science and the education of students. PFCs also include creative, substantive activities aimed at enhancing education, broadening participation of traditionally underrepresented groups, and outreach to the scientific community and general public.