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Student Cluster Algebra Seminar: Generalized Snake Graphs from Triangulated Orbifolds

Event Type
wifi event
Sep 8, 2021   4:00 pm  
Elizabeth Kelley, UIUC
Elizabeth Kelley

Abstract: We will continue the talk from last week. Cluster algebras, as originally defined by Fomin and Zelevinsky, are characterized by binomial exchange relations. A natural generalization of cluster algebras, due to Chekhov and Shapiro, allows the exchange relations to have arbitrarily many terms. For generalized cluster algebras that can be modeled by unpunctured triangulated orbifolds, we generalize the snake graph construction of Musiker, Schiffler, and Williams and obtain explicit combinatorial formulas for the Laurent expansion of any arc or closed curve. For ordinary arcs, this gives a combinatorial proof of positivity for the associated generalized cluster algebra. This talk is based on joint work with Esther Banaian.

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