Coding geodesic flows and various continued fractions

Merriman Claire (Illinois Math)

Abstract: Continued fractions are frequently studied in number theory, but they can also be described geometrically. I will give both pictorial and algebraic descriptions of the flows that describe continued fraction expansions. This talk will focus on continued fractions of the form a1±1a2±1a3±⋱, where the ai are odd. I will show how to describe these continued fractions as geodesic flows on a modular surface, and compare it to the modular surface needed when ai are even.