Title: Optimal Control, Geometry and Mechanics (1 hour)
Abstract: The Maximum Principle of optimal control has its roots in the Calculus of Variations of mechanics. Symmetry, in the form of Lie group actions on manifolds, plays a prominent role in mechanics, giving rise, for example, to the classical conservation laws. Differential geometry, especially symplectic geometry, provides a setting for both the Maximum Principle and for mechanics. In this talk, I will illustrate the rich interplay between all of these ideas.