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Dynamics, Geometry and Groups Seminar

Friday, November 18th, 2022

Time: 10:00 a.m.  Place: Jeffery Hall, Room 422

Speaker: Neil MacVicar (¾ÅÐãÖ±²¥)

Title: Computing Radix Expansions for Fractions of Gaussian Integers

Abstract: It is known that complex numbers can be written in base Gaussian integer b under conditions on both b and the coefficients of the powers of b (Katai and Szabo, 74). A representation of this kind is called a radix expansion. As per usual around these parts, the proof of the existence of an object does not always coincide with the object's construction - assuming the latter is even possible.

I will present an algorithm (Gilbert, 96) for determining the radix expansions of complex numbers whose real and imaginary parts are rational. Both the key and dynamical tie-in is that we want to leverage the iterated function system whose attractor is the set of expansions of negative powers of the base b.