Related papers: Hamiltonian linking and Symplectic packing

We prove that there are precisely two embedded exact Lagrangian fillings of the standard Legendrian Hopf link, up to compactly supported Hamiltonian isotopy. It was known that the standard Legendrian Hopf link admitted at least two such…

We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation…

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of…

We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robust, strong form of topological instability. We do not assume…

We introduce the notion of a Hamiltonian action of an \'etale Lie group stack on an \'etale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-Weinstein symplectic reduction theorem, and the…

We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…

We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating class of examples, this "symplectic Gysin sequence" is…

Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…

Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…

In this article we explore a symplectic packing problem where the targets and domains are $2n$-dimensional symplectic manifolds. We work in the context where the manifolds have first homology group equal to $\mathbb{Z}^n$, and we require…

Symplectic self-adjointness of Hamiltonian operator matrices is studied, which arises in symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The…

The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content…

In an earlier paper we explained how to convert the problem of symplectically embedding one 4-dimensional ellipsoid into another into the problem of embedding a certain set of disjoint balls into \CP^2 by using a new way to desingularize…

This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…

In this article we relate the construction of Ricci type symplectic connections by reduction to the construction of star product by reduction yielding rather explicit descriptions for the star product on the reduced space.

Motivated by an attempt to better understand the notion of a symplectic stack, we introduce the notion of a symplectic hopfoid, which should be thought of as the analog of a groupoid in the so-called symplectic category. After reviewing…

We show that a generic Hamiltonian diffeomorphism on a closed symplectic manifold which is symplectically aspherical has at least the stable Morse number of fixed points - this is in line with a conjecture by Arnold.

We consider strong symplectic fillings of the unit cotangent bundle of a hyperbolic surface, equipped with its canonical contact structure. We show that every finitely presentable group can be realised as the fundamental group of such a…

We observe that numerous symplectic resolutions can be expressed as intersections of twisted cotangent bundles. Additionally, their dual symplectic resolutions can be derived from intersections of dual twisted cotangent bundles. We…