Pint of Postdoc Speaker Recap - Dr. Taylor McAdam

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

Dr. Taylor McAdam

Edited by:

Jennifer Blackburn (assisted by Aileen Fernandez)

Abstract:

For Part 2 of April 2020 pint of postdoc, Taylor McAdam introduced the concept of hyperbolic geometry—a kind of geometry in which there is “more space” than the classical flat (or “Euclidean”) geometry that we learn about in school. In Euclidean geometry, given a line and a point lying off of that line, there is exactly one line parallel to the original line through that point. In hyperbolic geometry, there are infinitely many! She also introduced a dynamical system on this space called the geodesic flow, which represents what would happen if you started at a point in the space and simply walked forward. She shared what can happen under the geodesic flow if we cut up hyperbolic space and glue it back together in interesting ways, resulting in a system that demonstrates chaos!