However, the number theory seminar today is relevant to hyperbolic geometry:

Oklahoma State University 

Number Theory Seminar 

Title Binary Hermitian Forms and the Descartes Circle Theorem 

Speaker: David Wright, OSU 

Date: Sep 24, 2019 

Time: 3:30 PM 

Room: MSCS 422 

Abstract: Recently, there has been a lot of interest in Apollonian circle packings where the curvatures turn out to be integers, and the properties of the integers that occur as curvatures. We shall reframe this in terms of the binary hermitian forms corresponding to generalized circles and use that theory to derive the Descartes Four Circle Theorem, and similar theorems for other Kleinian circle packings. We shall use this to prove the curvatures in other Kleinian circle packings are algebraic integers in certain number fields.