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Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids
We obtain new sharp obstructions to symplectic embeddings of four-dimensional polydisks P ( a , 1) into four-dimensional ellipsoids E ( bc , c ) when
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On the existence of symplectic barriers
In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic...
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Symplectic Manifolds
In this chapter, we are going to see the definition of a symplectic manifold, several examples, and constructions of symplectic manifolds. We will...
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Full ellipsoid embeddings and toric mutations
This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in...
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Contact and Symplectic Geometry
The even-dimensional moment-angle manifolds and the LVM-manifolds have the characteristic that, except for a few, well-determined cases, they do not...
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On a Symplectic Bigraded Toda Hierarchy
In this paper, we construct a symplectic bigraded Toda hierarchy which contains an symplectic deformation of the original Toda lattice hierarchy. In...
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Quantitative h-principle in symplectic geometry
We prove a quantitative h -principle statement for subcritical isotropic embeddings. As an application, we construct a symplectic homeomorphism that...
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Asymptotically holomorphic theory for symplectic orbifolds
We extend Donaldson’s asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a compact symplectic orbifold such that...
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Remarks on asymptotic isometric embeddings of conic transforms for torus actions
Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given...
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Symplectic Geometry
Symplectic geometry is mainly motivated by the study of classical mechanics and dynamical systems. It can only be described for even-dimensional...
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Quantitative h-principle in symplectic geometry
We prove a quantitative h-principle statement for subcritical isotropic embeddings.
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Toric Degenerations in Symplectic Geometry
Toric degeneration in algebraic geometry is a process of degenerating a given projective variety into a toric one. Then one can obtain information...
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SYMPLECTIC PBW DEGENERATE FLAG VARIETIES; PBW TABLEAUX AND DEFINING EQUATIONS
We define a set of PBW-semistandard tableaux that is in a weight-preserving bijection with the set of monomials corresponding to integral points in...
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Singular symplectic spaces and holomorphic membranes
We set up a topological framework for degenerations of symplectic manifolds into singular spaces paying a special attention to the behavior of...
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Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines
We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each with one Seiberg–Witten basic class up to sign,...
