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Using modular surfaces to generate continued fractions

Claire Merriman
March 4, 2021
3:00PM - 4:00PM
Online: Zoom info below

Date Range
Add to Calendar 2021-03-04 15:00:00 2021-03-04 16:00:00 Using modular surfaces to generate continued fractions Speaker:  Claire Merriman (The Ohio State University) Title:  Using modular surfaces to generate continued fractions Speaker's URL:  https://www.asc.ohio-state.edu/merriman.72/ 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. URL associated with Seminar https://u.osu.edu/ergodictheory/ Additional Dates &/or Times Zoom link: https://osu.zoom.us/j/98033590349 Meeting ID: 980 3359 0349 Password: Mixing Online: Zoom info below Department of Mathematics math@osu.edu America/New_York public

Speaker:  Claire Merriman (The Ohio State University)

Title:  Using modular surfaces to generate continued fractions

Speaker's URL:  https://www.asc.ohio-state.edu/merriman.72/

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.

URL associated with Seminar
https://u.osu.edu/ergodictheory/


Additional Dates &/or Times
Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

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