Related papers: Dusa McDuff and symplectic geometry
We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…
This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).
We survey some recent progress on understanding when one four-dimensional symplectic manifold can be symplectically embedded into another. In 2010, McDuff established a number-theoretic criterion for the existence of a symplectic embedding…
In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.
We study the symplectic structure of the holomorphic coadjoint orbits, generalizing a theorem of McDuff on the symplectic structure of Hermitian symmetric spaces of noncompact type.
Sheaf theoretically based Abstract Differential Geometry incorporates and generalizes all the classical differential geometry. Here, we undertake to partially explore the implications of Abstract Differential Geometry to classical…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…
In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics, that provides a very short survey of derived symplectic geometry. Derived symplectic geometry studies symplectic structures on derived stacks.…
This is a survey on symplectic birational geometry. In arbitrary dimension, this subject is centered around the notion of uniruledness. In low dimensions, we will also discuss Kodaira dimension and minimality.
The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic…
The main goal of this paper is to give constructive proofs of several existence results for symplectic embeddings. The strong relation between symplectic packings and singular symplectic curves, which can be derived from McDuff's inflations…
This survey explores the geometry of three-dimensional Anosov flows from the perspective of contact and symplectic geometry, following the work of Mitsumatsu, Eliashberg-Thurston, Hozoori, and the author. We also present a few original…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical…