Topological and dynamical aspects of flows in fluid membranes

We will investigate hydrodynamic flows sourced by motors in
  fluid membranes. The membrane is modelled as a spherical monolayer of
  viscous fluid. The in-plane 2D fluid flows sourced by these motors
  are modelled as point defects, such as vortices and force dipoles. We
  will explore the effects of membrane curvature and topology on the
  flows sourced by these motors. We will explore the hydrodynamic
  interactions between them and discover interesting regimes of co-ordinated
  activity, vortex lattice formation, global rotation and aggregate
  formation in the fluid membrane interface. We will also present relevant
  simulations where several mathematical theorems such as Poincare Index
  theorem, Liouville-Arnold theorem and Kimura's conjecture will play a
  central role.