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Double-dimer configurations and quivers of dP3 (del Pezzo) type

Ponente: Gregg Musiker
Institución: University of Minnesota
Tipo de Evento: Investigación

Cuándo 17/11/2020
de 10:00 a 11:00
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.

NotaEsta 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.