Pint of Postdoc Speaker Recap - Dr. Caglar Uyanik

“Dynamics and Geometry: From Donuts to Hyperbolic Space (Part I)”

Dr. Caglar Uyanik

Edited by:

Jennifer Blackburn (assisted by Aileen Fernandez)

Abstract:

For Part I of April 2020 pint of postdoc, Caglar Uyanik discussed the fundamentals of dynamical systems—the study of the long-term behavior of systems that evolve in time according to fixed rules. He shared examples of rotations on a circle and linear flows on a torus (the shape that describes the surface of a donut) to see what different kinds of behaviors are possible. Given a point, does its trajectory under the flow close up and repeat itself?  Does it go everywhere? What kind of behavior should we expect if we pick a point at random? In trying to answer these questions, he showed that even relatively simple systems can have surprisingly complex behavior, leading to remarkable results!