Double-dimer configurations and quivers of dP3 (del Pezzo) type
Institución: University of Minnesota
Tipo de Evento: Investigación
Cuándo |
17/11/2020 de 10:00 a 11:00 |
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Dónde | https://paginas.matem.unam.mx/ocas |
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Double-dimer configurations and quivers of dP3 (del Pezzo) type
In this talk, I will describe our work extending combinatorial interpretations for so called toric cluster variables as was previously studied by myself and Tri Lai. In [LM 2017] and [LM 2020], most toric cluster variables were shown to have Laurent expansions agreeing with partition functions of dimers on subgraphs cut out by six-sided contours. However, the case of cluster variables parameterized by six-sided contours with a self-intersection eluded our techniques. In this talk we discuss our research rectifying this issue by using Helen Jenne’s condensation results for the double-dimer model [J 2019]. While we focus on quivers of dP3 type of Model 1 and Model 4, we anticipate our techniques will extend to certain additional cluster algebras related to brane tilings. This is joint work with Helen Jenne and Tri Lai.
Nota: Esta charla es parte del Online Cluster Algebra Seminar organizado por Anna Felikson, Michael Gekhtman, Daniel Labardini-Fragoso, Kyungyong Lee, Pierre-Guy Plamondon, Ralf Schiffler y Khrystyna Serhiyenko.