Circles of Apollonius two ways

Abstract: There are eight circles tangent to a given trio of circles, provided that one works over the complex numbers. Over the reals, some of these tangent circles can go missing. In order to obtain an invariant count of tangent circles, one needs to count each tangent circle with an appropriate weight. I will talk about two geometric characterizations of such counting weights, as well as how to use these counting weights over any field of characteristic not 2.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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