- This event has passed.
Colloquium – Gordana Todorov (Northeastern University)
March 30, 2021 @ 11:00 am - 12:00 pm
Title: Friezes, Quiver Representations and Cluster Theory
Abstract: After cluster algebras were introduced by Fomin and Zelevinsky, there were
many new connections found among many fields of mathematics: combinatorics,
representation theory, quiver representations, non-commutative algebra, poisson
theory and much more.
Friezes were introduced by Conway and Coxeter as a very combinatorial
notion. Since the introduction of cluster theory, there is a new interest in
friezes and their relation to cluster and representation theory. First, I will
recall definitions and relations between finite friezes, triangulations of polygons,
representations of quivers of Dynkin type A and associated cluster categories,
all of which are known results.
More recent results are about infinite friezes. It is known that any infinite
frieze comes from a triangulation of an annulus. Furthermore every triangulation
of an annulus defines a pair of friezes. First we show that to each infinite frieze
there are infinitely many triangulations and hence friezes which can form a pair
for a triangulation. However when considering skeletal friezes, one infinite frieze
uniquely determines another skeletal frieze which form a pair for a triangulation.
The ideas and proofs are done using representations of affine quivers of Dynkin
type A~.