Related papers: Prime-localized Weinstein subdomains

This paper establishes an isomorphism between endomorphism algebras from the wrapped Fukaya category of a type of punctured surface, and the class of A-infinity algebras related to bordered knot Floer homology, called star algebras, which…

Given a closed, oriented Lagrangian submanifold $L$ in a Liouville domain $\overline{M}$, one can define a Maurer-Cartan element with respect to a certain $L_\infty$-structure on the string homology…

We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya…

The eigenstates of a quantum spin glass Hamiltonian with long-range interaction are examined from the point of view of localisation and entanglement. In particular, low particle sectors are examined and an anomalous family of eigenstates is…

We consider a version of the relative Fukaya category for anticanonical Lefschetz pencils. There are direct connections between the behaviour of this category and enumerative geometry: some of these are results announced here, others remain…

We consider the Poisson reduced space $(T^*Q)/K$ with respect to a cotangent lifted action. It is assumed that $K$ is a compact Lie group which acts by isometries on the Riemannian manifold $Q$ and that the action on $Q$ is of single…

We study symplectic invariants of the open symplectic manifolds $X_\Gamma$ obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree $\Gamma$. For any tree $\Gamma$, we calculate (DG-)algebra models of the Fukaya…

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.

Moduli spaces of semi-stable real and quaternionic vector bundles of a fixed topological type admit a presentation as Lagrangian quotients, and can be embedded into the symplectic quotient corresponding to the moduli variety of semi-stable…

The Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. If true, it would give tight quantitative bounds relating combinatorial and algebraic notions of approximate subgroups. In this note, we…

Let $M$ be a Liouville 6-manifold which is the smooth fiber of a Lefschetz fibration on $\mathbb{C}^4$ constructed by suspending a Lefschetz fibration on $\mathbb{C}^3$. We prove that for many examples including stabilizations of Milnor…

It is known that any closed, exact Lagrangian in the cotangent bundle of a closed, smooth manifold is of the same homotopy type as the zero section. In this paper, we give a Fukaya-theoretic proof of this fact for the sphere and torus to…

This paper discusses the cobordism of Lagrangian submanifolds (in the monotone setting) and structures it as a category that is related in a functorial way to an appropriate (derived) Fukaya category. Are also discussed obstructions to…

These are notes from a 2010 talk. They concern possible ways in which Fukaya categories might be considered as "local", which means glued together from simpler pieces in a loosely sheaf-theoretic sense. As the title suggests, this is purely…

Given an exact symplectic manifold M and a support Lagrangian \Lambda, we construct an infinity-category Lag, which we conjecture to be equivalent (after specialization of the coefficients) to the partially wrapped Fukaya category of M…

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

Let X be a compact complex manifold, $D_c^b(X)$ be the bounded derived category of constructible sheaves on $X$, and $Fuk(T^*X)$ be the Fukaya category of $T^*X$. A Lagrangian brane in $Fuk(T^*X)$ is holomorphic if the underlying Lagrangian…

We introduce a new way to encode semicyclic structures using a stack of broken cycles. (We also prove an analogue for paracyclic structures.) This was motivated not only by higher algebra but also by Fukaya-categorical considerations. We…

We show that any quasi-Gorenstein deformation of a $3$-dimensional quasi-Gorenstein Buchsbaum local ring with $I$-invariant $1$ admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings…

A fundamental and deep result in symplectic topology due to Abouzaid and Kragh states that the Maslov class vanishes for closed exact Lagrangians in cotangent bundles of closed manifolds. In this article we prove by an explicit construction…