Related papers: Simultaneous linear symplectic reduction and orbit…

We found some Lagrangian submanifolds of the adjoint semisimple orbit in two cases. For the first, the compact case, also known as the Generalized flag manifolds, we prove that the real flags can be seen as infinitesimally tight Lagrangian…

We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…

In the present paper, we obtain real-analytic symplectic normal forms for integrable Hamiltonian systems with $n$ degrees of freedom near singular points having the type ``universal unfolding of $A_n$ singularity'', $n\ge1$ (local…

We give a coadjoint orbit's diffeomorphic deformation between the classical semisimple case and the semi-direct product given by a Cartan decomposition. The two structures admit the Hermitian symplectic form defined in a semisimple complex…

Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the…

Our project is to define Radon-type transforms in symplectic geometry. The chosen framework consists of symplectic symmetric spaces whose canonical connection is of Ricci-type. They can be considered as symplectic analogues of the spaces of…

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also…

We study symplectic rigidity phenomena for fibers in cotangent bundles of Riemann surfaces. Our main result can be seen as a generalization to open Riemann surfaces of arbitrary genus of work of Eliashberg and Polterovich on the Nearby…

There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold $(M,\sigma)$, compared to the standard case of a symplectic manifold: in the almost-symplectic case, a vector field such that the…

It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in…

We study the moduli spaces of polygons in R^2 and R^3, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gel'fand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson…

Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by…

We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the…

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…

Seidel-Smith and Manolescu constructed knot homology theories using symplectic fibrations whose total spaces were certain varieties of matrices. These knot homology theories were associated to $SL(n) $ and tensor products of the standard…

We show that the space of anti-symplectic involutions of a monotone $S^2\times S^2$ whose fixed points set is a Lagrangian sphere is connected. This follows from a stronger result, namely that any two anti-symplectic involutions in that…

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a…

The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…

We consider moduli spaces of cyclic configurations of $N$ lines in a $2n$-dimensional symplectic vector space, such that every set of $n$ consecutive lines generates a Lagrangian subspace. We study geometric and combinatorial problems…