Related papers: Symplectic higher Auslander correspondence for typ…

We prove that the Fukaya-Seidel categories of a certain family of Lefschetz fibrations on $\mathbb{C}^2$ are equivalent to the perfect derived categories of Auslander algebras of Dynkin type $\mathbb{A}$. We give an explicit equivalence…

We show that the perfect derived categories of Iyama's $d$-dimensional Auslander algebras of type $\mathbb{A}$ are equivalent to the partially wrapped Fukaya categories of the $d$-fold symmetric product of the $2$-dimensional unit disk with…

We prove that the derived Fukaya category of the Lefschetz fibration defined by a Brieskorn-Pham polynomial is equivalent to the triangulated category of singularities associated with the same polynomial together with a grading by an…

We realise Stroppel's extended arc algebra in the Fukaya-Seidel category of a natural Lefschetz fibration on the generic fiber of the adjoint quotient map on a type $A$ nilpotent slice with two Jordan blocks, and hence obtain a symplectic…

We describe a construction of the Fukaya category of an exact symplectic Lefschetz fibration, together with its closed-open string map.

To a symplectic Lefschetz pencil on a monotone symplectic manifold, we associate an algebraic structure, which is a pencil of categories in the sense of noncommutative geometry. One fibre of this "noncommutative pencil" is related to the…

It follows from the work of Burban and Drozd arXiv:0905.1231 that for nodal curves $C$, the derived category of modules over the Auslander order $\mathcal{A}_C$ provides a categorical (smooth and proper) resolution of the category of…

We prove that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We then describe the topology of the regular and singular fibres, in particular calculating their middle Betti numbers. For the…

We prove homological mirror symmetry for Lefschetz fibrations obtained as disconnected sums of polynomials of types A or D. The proof is based on the behavior of the Fukaya category under the addition of a polynomial of type D.

We develop a novel combinatorial perspective on the higher Auslander algebras of type $\mathbb{A}$, a family of algebras arising in the context of Iyama's higher Auslander-Reiten theory. This approach reveals interesting simplicial…

We extend Auslander--Iyama correspondence to the setting of exact dg categories. By specializing it to exact dg categories concentrated in degree zero, we obtain a generalization of the higher Auslander correspondence for exact categories…

We prove that a positive allowable Lefschetz fibration, PALF in short, admits a structure of exact Lefschetz fibration in the sense of Seidel \cite{Se08}. If the two-fold first Chern class of the total space is zero, we obtain the…

We investigate a possible theory of higher Fukaya categories associated to $n$-shifted symplectic stacks, where $n \geq 0$. We consider two paradigmatic cases, the shifted cotangent stack of a smooth manifold and the coadjoint stack of a…

We prove that the bounded derived category of the lattice of order ideals of the product of two ordered chains is fractionally Calabi-Yau. We also show that these lattices are derived equivalent to higher Auslander algebras of type A. The…

We give an introduction to partially wrapped Fukaya categories of surfaces with orbifold singularities. Dissecting an orbifold surface $\mathbf S$ into polygons, certain dissections give rise to formal generators, inducing a triangulated…

Inspired by the recent work of Henrard, Kvamme and van Roosmalen [17], we prove a categorified version of higher Auslander correspondence in the context of exact categories. We define n-Auslander exact categories and show that there is a…

This article consists of an introduction to Iyama's higher Auslander-Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander-Reiten theory,…

We show that every higher Auslander algebra $A_{n+1}^d$ of type $\mathbb{A}$ such that $\gcd(n,d)=1$ is derived equivalent to a certain replicated algebra $B=B_0^{(n+d)}$. Moreover ${\rm{gldim}} B = nd$ and $B$ admits an $nd$-cluster…

We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow (math/0604379,…

We work over a perfect field. Recent work of the third-named author established a Derived Auslander Correspondence that relates finite-dimensional self-injective algebras that are twisted $3$-periodic to algebraic triangulated categories of…