Title: Using modular surfaces to generate continued fractions
Speaker: Claire Merriman – The Ohio State University
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 $a_1\pm\frac{1}{a_2\pm\frac{1}{a_3\pm\ddots}}$, where the $a_i$ are odd. I will show how to describe these continued fractions as geodesic on the hyperbolic plane, and how they cross cells of the Farey tessellation.
Zoom link: https://osu.zoom.us/j/98033590349
Meeting ID: 980 3359 0349
Password: Mixing
Recorded talk: https://osu.zoom.us/rec/play/FNCFPum1mokl6Bnf8uJ76iRehQRPNq5Op3VMXBDbNz7lAPb5qGWwnud4KJJucCuZQhrufoMV3d7X7MbK.icd0xSMxEksuitng?continueMode=true&_x_zm_rtaid=TxJ_aekJTv69MOkCQOL-dA.1614920606908.f7398a7dd87a1fb116574333eca30d89&_x_zm_rhtaid=489