Abstract

Continued fractions have proven themselves as although ancient, remarkably useful tools in many distinct areas. The topic has quite a rich history. The study of continued fractions is treated in two cases: real and complex. In the first part of this talk we give a summary of real continued fractions from an algebraic and geometric point of view. In the second part we will discuss the current work to generalize what is known for real continued fractions to the complex case. More precisely, we will be considering continued fractions over norm-Euclidean imaginary quadratic fields. This is a work in progress and a joint work with Ersin Süer and Ayberk Zeytin.

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