| Abstract: |
| Cluster algebras in the skew-symmetric case admit a powerful categorification through representations of quivers with potentials, following the work of Derksen-Weyman-Zelevinsky. Extending this picture to the skew-symmetrizable case remains an important open problem. Modulated graphs with potentials generalize quivers with potentials and thus provide a promising candidate for such an extension. In this talk, I will present a mutation theory for modulated graphs with potentials and discuss how their representations may be used to categorify certain skew-symmetrizable cluster algebras. The goal is to suggest a representation-theoretic framework that parallels the skew-symmetric theory while capturing new phenomena arising in the skew-symmetrizable setting. |
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