Seminar 8.30.18 Vandehey

Title: Ergodicity of Iwasawa continued fractions

Speaker: Joseph Vandehey (The Ohio State University)

Abstract: The connections between the behavior of geodesic flow on the modular surface and the Gauss map for the regular continued fraction expansion date back to Artin. Recently, Anton Lukyanenko and myself were able to extend this connection to higher dimensional hyperbolic spaces and higher dimensional continued fraction algorithms. This allows us to give proofs of ergodicity for a variety of new continued fraction expansions, including quaternionic, octonionic, and Heisenberg continued fractions. We will discuss this result and some of the odd consequences of it.