Cluster categories from Fukaya categories

Abstract: The wrapped Fukaya category of the plumbing X of the cotangent bundles of spheres along a tree T is shown to be quasi-equivalent to the dg category of dg modules over the Ginzburg dg algebra associated to a quiver Q whose underlying graph is T. In this talk, I will first discuss that the quotient of the wrapped Fukaya category W of X by its compact Fukaya category F is equivalent to the Amiot–Guo–Keller cluster category associated to Q, and a certain generator L of W becomes a cluster-tilting object of W/F. Then using the minimal model of the Ginzburg dg algebra computed by Hermes, in the case the tree T is given by a Dynkin diagram of type A,D or E, I will explain how to show that the endomorphism algebra of L in the quotient category W/F is isomorphic to the path algebra of a certain quiver with relations. This talk is based on a joint work with Wonbo Jeong and Jongmyeong Kim.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

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