September 5, 2013
The mathematical theory of optimal control was first formalized by the Russian mathematician Lev Pontryagin in the late 1950s. Since then, the theory has been applied to a remarkably wide range of problem areas, including space craft navigation, cancer therapy design, and natural resource management, to name a few. As a subject that is widely practical but mathematically and computationally sophisticated, it represents a natural axis for collaborative work between applied mathematicians and scientists from other disciplines.
In this talk, which is designed for a general audience, I begin with a tutorial introduction to several key ideas from the theory of optimal control. I then sketch examples of how these ideas have played out in my recent collaborative research within a “working group” sponsored by the National Institute for Mathematical and Biological Synthesis (NIMBioS.) Our working group contains mathematicians, ecologists, economists, and computer scientists, and I spend some time discussing both the challenges and the rewards of our cross-disciplinary dialogue. By highlighting examples of undergraduate involvement and illustrating the broad nature of the work, I hope to encourage students and faculty to consider potential applications of this subject to their own research problems.