Summary
Symmetries play an important role in understanding any complex system, and this project will further the understanding of symmetries in a field of mathematics called symplectic geometry. Tie a ball to a string, hold the string up, and give the ball a push. Can you predict how the ball will swing? Though it has now extended far beyond its roots, symplectic geometry was originally developed to study classical dynamical systems, such as this pendulum. To predict its motion, it is useful to notice that while the position and velocity of the pendulum change over time, the values of both the total e
