Tuesday, November 27, 14:00, 7.527

Ilke Canakci (Newcastle), Cluster algebras and continued fractions

Abstract:
I will report on a connection between cluster algebras and continued fractions which is given in terms of so-called 'snake graphs'. Snake graphs are planar graphs first appeared in the context of cluster algebras associated to marked surfaces. In their first incarnation, they were used to give formulas for generators of cluster algebras. Along with further investigations and several applications, they were also studied from a more abstract point of view as combinatorial objects. This talk will focus on a combinatorial realisation of continued fractions in terms of 'perfect matchings' of snake graphs. I will also discuss applications to cluster algebras, elementary number theory and, time permitting, to knot theory. This is joint work with Ralf Schiffler.