Geometry, Mechanics, and Biology Applications for Membranes and Filaments

Nature displays a vast array of geometrically ordered systems, at nearly every length scale. This is especially true in soft matter and biological physics, where geometric
considerations help us understand problems from the assembly of helical proteins to the morphogenesis of
flower petals. In many cases, this geometric ordering is
mechanical in origin: energy must be expended for objects to stretch, bend, and deform. This thesis explores some of the conclusions that can be drawn from this simple observation.