Frieze patterns in algebra, combinatorics and geometry / Frises en algèbre, combinatoire et géométrie

Collection Frieze patterns in algebra, combinatorics and geometry / Frises en algèbre, combinatoire et géométrie

Organisateur(s) Baur, Karin ; Cuntz, Michael ; Faber, Eleonore ; Plamondon, Pierre-Guy

Date(s) 12/05/2025 - 16/05/2025

URL associée https://conferences.cirm-math.fr/3214.html

00:00:00 / 00:00:00

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Frieze patterns and representation theory

De Khrystyna Serhiyenko

The goal of this talk is to explore the connections between various frieze patterns and representation theory of associative algebras. We begin with the classical Conway- Coxeter friezes over positive integers and their correspondence with Jacobian algebras of type A, where entries in the frieze count the number of submodules of indecompos- able representations. This can also be reinterpreted in terms of applying the Caldero- Chapoton map, providing a close connection to Fomin-Zelevinsky's cluster algebras. Extending these ideas beyond the classical case, we will also discuss higher dimen- sional friezes, called (tame) SLk friezes, as well as their relation to cluster algebras on coordinate rings of Grassmannians Gr(k,n) and their categorification. Furthermore, SLk friezes are a special type of SLk tilings, integer tilings of the plane satisfying the condition that every k x k square has determinant 1. We will present a characterization of SLk tilings in terms of pairs of bi-infinite sequences in Zk and discuss applications to duality and positivity.

Informations sur la vidéo

Date de captation 12/05/2025
Date de publication 04/06/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20346503
Citer cette vidéo Serhiyenko, Khrystyna (12/05/2025). Frieze patterns and representation theory . CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20346503
URL https://dx.doi.org/10.24350/CIRM.V.20346503

Domaine(s)

Bibliographie

ZACHERY Peterson et SERHIYENKO Khrystyna, SLk -tilings and paths in Zk , preprint arXiv: 2504.01693, 2025, 30 pp. - https://doi.org/10.48550/arXiv.2504.01693
BAUR, Karin, FABER, Eleonore, GRATZ, Sira, et al. Friezes satisfying higher SLk-determinants. Algebra & Number Theory, 2021, vol. 15, no 1, p. 29-68. - https://doi.org/10.2140/ant.2021.15.29
CALDERO, Philippe et CHAPOTON, Frédéric. Cluster algebras as Hall algebras of quiver representations. Commentarii Mathematici Helvetici, 2006, vol. 81, no 3, p. 595-616. - https://doi.org./10.4171/cmh/65

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