[Geom., Alg. & Phys.] Modulated graphs with potentials and skew-symmetrizable cluster algebras
ABSTRACT
Cluster algebras in the skew-symmetric case admit a powerful categorification via 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 generalize quivers in the sense of Dlab–Ringel, but incorporating potentials into their representation theory remains challenging. In this talk, I will describe a framework of modulated graphs over symmetric Frobenius algebras with potentials and develop a corresponding mutation theory. I will then explain how this framework leads to a categorification of certain skew-symmetrizable cluster algebras. (https://sites.google.com/view/gapkias)
