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Ober­se­mi­nar Al­ge­bra und Al­ge­brai­sche Geo­me­trie: Esther Ba­nai­an (Pa­der­born): Ge­ne­ra­li­zed clus­ter va­ri­a­bles and Cal­de­ro-Cha­po­ton func­ti­ons

Ort: A3.339

Abstract: From a triangulated surface, one can construct both a cluster algebra and a gentle algebra. Musiker–Schiffler–Williams and Geiß–Labardini-Fragoso–Schröer showed that cluster variables of the former coincide with Caldero-Chapoton functions of the latter. We will review this narrative and discuss how the statement can be extended to the case of a triangulated orbifold, using Chekhov–Shapiro’s generalization of a cluster algebra. This is based on separate joint work with Kelley and with Valdivieso.