Math Mornings: Chaos on the Circle, by Taylor McAdam

Rotate a circle by a fixed angle, then repeat again and again.  Where will a single point travel? Will it come back to where it started and how does the answer depend on the rotation angle?  Rotations and other transformations of the circle teach us a lot about many processes like planets orbiting a sun, coffee stirred in a cup, and about the very nature of numbers themselves.  In this talk, Taylor McAdam, NSF postdoctoral fellow at Yale, discusses a variety of ways that mathematicians think about how “complicated" or chaotic such a process becomes.  Along the way we find surprising connections to other areas of math such as (ir)rationality of real numbers and decimal or binary sequences.