Tuesday, November 27, 14:00, 7.527
Ilke Canakci (Newcastle), Cluster algebras and continued fractions
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.