This workshop will focus on geometry, topology and their applications to control systems. Control theory deals with the problem of shaping the behavior of "systems", which can mean an engineered object, such as a robotic arm used for remote surgery, or a natural one, such as a flock of birds or even the brain. The basic driving questions are how to control or design a system which performs as desired. Geometric and topological ideas have led to technological breakthroughs throughout the years, but geometric thinking in engineering has not yet permeated the mainstream. The goal of this workshop is to bring together a diverse group of engineers and scientists working in geometry, topology and their intersection, in order to open new frontiers of research and applications.