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<br>considerations help us understand problems from the assembly of helical proteins to the morphogenesis of <br>flower petals. In many cases, this geometric ordering is<br>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.<br>