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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~.

Details

Date:
March 30, 2021
Time:
11:00 am - 12:00 pm
Event Category:
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