Mathematics Colloquia and Seminars

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Classical Apollonian circle packings are constructed from a quadruple of pairwise tangent circles on a plane by successively inscribing circles into the triangular interstices. In this expository talk, we explain the hyperbolic geometry behind these packings in terms of the upper half-space model and the projective disk/hyperboloid models, and then describe the symmetry group of these packings as a subgroup of the isometry group of hyperbolic space and as a subgroup of the orthogonal group of the Descartes quadratic form.