In this talk, Dr. Shelley will discuss the interaction of a viscous fluid with elastic filament; a problem of fundamental importance in physics and biology (e.g., biological fibers, motility of microorganisms, phase-transition of liquid crystals). Motivated by the pattern formation during the growth of liquid crystals in isotropic smectic-A phase transition, Dr. Shelley will consider the nonlocal Stokesion (inertialess) dynamics of a growing elastic filament immersed in a fluid. The nonlocal interactions of the filament with itself are taken into account by a modification of Keller-Rubinow's slender body-theory. Given this new formulation, Dr. Shelley will show that there exists a buckling instability driven by the growth of the filament. Eventually, the coupling of the buckling instability with the non-local interaction of the filament with itself and the fluid leads to a space-filling labyrinthine pattern. Theoretical predictions and new numerical methods will be used to study the long-time dynamics of the system. (Abstract by A. Goriely).