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An Algebraic Variety Related to Tau-Tilting Theory

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CARW03 - Interdisciplinary applications of cluster algebras

Let A be a finite-dimensional algebra of finite representation type. I will describe an affine algebraic variety whose totally non-negative part reflects the combinatorics of the tau-tilting fan of A. Starting from a Dynkin quiver, one obtains something closely related to the corresponding Fock–Goncharov cluster X variety, while in general, points on (one component of) the variety can be given in terms of ratios of F-polynomials; the upshot is that this construction can be viewed as an extension of some of the beautiful features of cluster algebras to a more general setting.

This talk is part of the Isaac Newton Institute Seminar Series series.

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