Wednesday, October 13, 2021
10/13/2021 - 2:30pm
10/13/2021 - 4:00pm
The Putnam seminar meets every Wednesday from 4 to 5:30 in LOM 214. As always, everyone is warmly welcomed to come to hang out, learn more cool math, and meet folks. The seminar is casual, and folks can come and go as they like. See Pat Devlin’s webpage (and/or contact him) for more information. Folks can sign up for the mailing list here: https://forms.gle/nYPx72KVJxJcgLha8
10/13/2021 - 4:15pm
Given a polygon in the Euclidean or hyperbolic plane, its billiard flow on the tangent bundle has trajectories that describe the paths of particles in the polygon (the billiard trajectories) traveling along straight lines and “bouncing” off the sides. Labeling the sides of the polygon the billiard flow determines a symbolic coding we call the bounce spectrum, which is the set of biinfinite sequences of labels corresponding to the sides encountered by all trajectories. A natural question asks the extent to which the bounce spectrum determines the shape of the polygon. For both Euclidean and hyperbolic polygons, there are nontrivial constructions of polygons with the same bounce spectrum that are not isometric/similar. In this talk, I’ll describe these constructions, and then results of joint work with Duchin, Erlandsson, and Sadanand stating that these are in fact the only ways in which non-isometric/non-similar polygons can have the same bounce spectrum.