Title: Geometry, Robots and Society

Abstract: How do we move a robot quickly from one position to another? To answer this question, we need to understand its configuration space, a "map" where we can find every possible position of the robot. Unfortunately, these spaces are very large, they live in very high-dimensions, and they are very difficult to visualize. Fortunately, geometric group theorists and combinatorialists have encountered and studied similar spaces before. Thanks to the tools they've developed, we can build "remote controls" to navigate these complicated spaces; this allows us to move (some) robots optimally. As the imaginary border between "pure" and "applied" mathematics disappears before our eyes, we face an important ethical question that we cannot ignore: What’s the role of mathematicians and scientists in building a more just and equitable society?

This presentation will assume no previous knowledge of these topics, and will be accessible to anyone who is interested. It will include joint work with many people, including Tia Baker, Naya Banerjee, Hanner Bastidas, César Ceballos, John Guo, Megan Owen, Seth Sullivant, Coleson Weir, and Rika Yatchak.