Francesca Fedele
(University of Leeds)

Mathematics Seminar

In the study of cluster algebras, computing cluster variables explicitly is an important problem. For surface cluster algebras, one can do so combinatorially using dimer covers of snake graphs. Recent work by Musiker, Ovenhouse and Zhang extend the theory in an attempt to define "super" cluster algebras of type A. The authors give a combinatorial formula, using double dimer covers of snake graphs to compute super lambda lengths in Penner-Zeitlin's super Teichmuller spaces. In the classic surface cluster algebras setting, one can alternatively use a representation theoretic approach to compute cluster variables using the CC-map. Motivated by this, we introduce a representation theoretic interpretation of super lambda-lengths and a super CC-map which agrees with the combinatorial formula by Musiker, Ovenhouse and Zhang. This is a joint work in progress project with Canakci, Garcia Elsener and Serhiyenko.

Organised by: AarHomAlg