**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