Samantha Fairchild, University of Washington
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Abstract: Inspired by Dirichlet's Approximation Theorem, we will introduce and prove Hurwitz's Theorem, a number theoretic result on approximating irrational numbers by rational numbers. To prove this theorem, we will use hyperbolic geometry. This will be a small example of techniques in homogeneous dynamics, which frequently use dynamics and geometry in order to prove number theoretic results.