Toric Promotion with Reflections and Refractions

Explore a cutting-edge lecture on combinatorial dynamics presented by Colin Defant of Harvard University at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the innovative concept of toric promotion with reflections and refractions, a generalization inspired by recent work on refraction billiards. Discover how this dynamical system discretizes a billiards system where light interacts with toric hyperplanes through reflection, refraction, and transmission. Learn about the simple formula for orbit structure when the underlying graph is a forest, and uncover new insights into orbit sizes for cycles with even numbers of refraction edges. Encounter an intriguing instance of the cyclic sieving phenomenon in specific graph configurations. Gain valuable knowledge about this collaborative research with Ashleigh Adams and Jessica Striker, pushing the boundaries of algebraic combinatorics and dynamical systems.

Colin Defant - Toric Promotion with Reflections and Refractions - IPAM at UCLA