Farey-Ford Packings are a special case of more general circle packings called Apollonian Circle Packings (ACP). These packings have some very interesting properties, for exmaple, if any four mutually tangent circles have integer curvatures, then so do all others in the packing. This has led to many important problems like prime number theorem in this setting. Kontorovich and Oh explore it from dynamics point of view whereas Bourgain, Fuchs and Sarnak look at them more number theoretically. In this talk, our focus will be on the specialized packings Farey-Ford Packings. We consider some basic statistics associated to these circles and answer some questions about their distributions and asymptotic behavior. One can ask similar questions in the general setting for ACP, and if time permits, we will discuss it in this talk. Some of this is joint work with Athreya, Chaubey and Zaharescu.

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Last updated: 11 Dec 2023