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Thursday, May 7, 2015

**Abstract:** Let $K$ be an imaginary quadratic field with ring of integers OK. The Schmidt arrangement of $K$ is the orbit of the extended real line in the extended complex plane under the Bianchi group $PSL(2,OK)$ (realised as Mobius transformations). The arrangement takes the form of a dense collection of intricately nested circles. I'll explain how the number theory of $K$ influences the arrangement, and I'll use these arrangements to generalise Apollonian circle packings and define a new collection of thin groups of arithmetic interest.