Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories

Abstract: The theme of this talk will be to build a bridge between two areas of mathematics: representation theory and symplectic geometry. Our objects of interest on the representation theoretical side are Auslander algebras of type A. This family of non-commutative algebras arises very naturally as endomorphism algebras of indecomposable modules of quivers of finite type. They were given a symplectic interpretation by Dyckerhoff-Jasso-Lekili, who proved the equivalence (as $A_{\infty}$-categories) between perfect derived categories of Auslander algebras of type A and certain partially wrapped Fukaya categories. We use their result to prove an equivalence between the categories in question and the Fukaya-Seidel categories of a certain family of Lefschetz fibrations. In this talk, we will observe this result in some key examples.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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