Department of Mathematics

Seminar in Cluster algebras

  •  Nicholas Ovenhouse, Yale University
  •  Super Cluster Algebras from Surfaces
  •  11/14/2022
  •  12:30 PM - 1:30 PM
  •  C304 Wells Hall
  •  Linhui Shen (shenlin1@msu.edu)

One of the most well-known examples of a cluster structure comes from Penner's lambda-length coordinates on the decorated Teichmuller space of a surface. In 2019, Penner and Zeitlin defined a super-manifold generalizing the decorated Teichmuller space, which involves new anti-commuting variables. I wall talk about some recent work with Gregg Musiker and Sylvester Zhang, where we showed that the coordinates on the decorated super Teichmuller space have many of the nice properties associated to a cluster structure, such as a kind of Laurent phenomenon, positivity, and some interesting combinatorial interpretations of the Laurent expressions, involving double dimer covers of certain graphs.

 

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Department of Mathematics
Michigan State University
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