In 2012, Lam and Pylyavskyy introduced Laurent phenomenon (LP) algebras. These algebras are a generalization of cluster algebras where the Laurent phenomenon still holds. However, it is not known if positivity holds for these algebras. In this talk, we define graph LP algebras, a type of LP algebra that can be defined combinatorially using a graph. We then describe a snake graph construction that allows us to find a combinatorial expansion for a large class of the cluster variables. Our construction proves positivity for certain cluster variables. This is joint work with Esther Banian, Elizabeth Kelley, and Sylvester Zhang.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974