The Graham group uses theory and computations to study problems in fluid dynamics, rheology and transport phenomena over a wide range of scales. We focus on problems that hold both fundamental interest in advancing basic principles as well as impact on applications. The group has two basic thrust areas, one in microscale flows and complex fluids and the other in the nonlinear dynamics of turbulent flows. In the first area, we are interested in general in the dynamics of mechanically and geometrically complex objects suspended in a flowing fluid and the interplay between microstructure and flow. Specific examples under study include the dynamics of blood cells in flow, the interplay between cell geometry and mechanics in bacterial swimming, the deformations of thin deformable sheetlike particles in flow, and the rheology and fluid dynamics of dilute micellar surfactant solutions. In the area of turbulent flows, the group aims to elucidate the complex interaction between rheology and fluid dynamics that leads to the phenomenon of turbulent drag reduction in polymer and surfactant solutions — this topic is a bridge to the group’s interest in microscale flows and rheology. We also apply ideas from nonlinear dynamical systems theory, data science and machine learning to elucidate the principles underlying the complex dynamics of turbulent shear flows, aiming toward development of control schemes that can manipulate turbulence to desired ends such as drag reduction.