Carl Toews
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.