Geometry MMA Seminar: Geodesic flows and slow downs of continued fraction maps

Speaker:  Claire Merriman, Davidson College

Title:   Geodesic flows and slow downs of continued fraction maps

Abstract:  We will start by looking at the Farey tent-map as a slowdown of the Gauss map for the regular continued fractions. The connection between cutting sequences of geodesics on the modular surface $PSL(2,\mathbb{Z})\backslash\mathbb{H}$ and regular continued fractions was established by Series, and Heersink expanded the cross-section of the geodesic flow on the unit tangent bundle for the Farey map. I will look at explicitly connecting Heersink's cross-section with Series' cutting sequence description.

I will then describe the slowdown of the even Gauss map using cutting sequences of geodesics on the modular surface $\Theta\backslash\mathbb{H}$ and even continued fractions. This modular surface has two cusps, slightly complicating the geometric description of the cutting sequences.

Time: Tuesday, October 10, 2023 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106