Conway-Coxeter friezes and combinatorics of curve singularities

Abstract: Conway-Coxeter friezes are arrays of positive integers satisfying a determinantal condition, the so-called diamond rule. Recently, these combinatorial objects have been of considerable interest in representation theory, since they encode cluster combinatorics of type A. In this talk I will discuss a new connection between Conway-Coxeter friezes and the combinatorics of a resolution of a complex curve singularity: via the beautiful relation between friezes and triangulations of polygons one can relate each frieze to the so-called lotus of a curve singularity, which was introduced by Popescu-Pampu. This allows to interprete the entries in the frieze in terms of invariants of the curve singularity, and on the other hand, we can see cluster mutations in terms of the desingularization of the curve. This is joint work with Bernd Schober.