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Friday, December 8, 2017

**Abstract:** Continued fractions are frequently studied in number theory, but they can also be described by geodesics on modular surfaces. This talk will look at 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, and how to use geodesic flows to represent the digits.