Dylan Crook (University of Leeds) – Curve Singularities, Coxeter-Conway Friezes and Continued Fractions

Coxeter-Conway friezes and their generalisations are of interest to many mathematicians, largely thanks to their well-known connections to cluster theory and representation theory. Many such connections are motivated by the beautiful correspondence, discovered by Coxeter and Conway, between these frieze patterns and triangulations of polygons. By way of this this same correspondence, we may also make connections between these friezes and other areas of mathematics - in this talk, we discuss a connection between (particularly nice) plane curve singularities and the theory of Coxeter-Conway friezes via an invarant known as the lotus of a plane curve singularity. We will also see how the continued fraction representations of rational numbers appear in this construction.