The -graded symplectic Floer cohomology of monotone Lagrangian submanifolds.
The Gromov invariant and the Donaldson-Smith standard surface count.
The Gromov width of complex Grassmannians.
The group of quasisymmetric homeomorphisms of the circle and quantization of the universal Teichmüller space.
The image in of the set of closed 2-forms with preassigned kernel
The infinitesimal counterpart of tangent presymplectic groupoids of higher order
Let be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, where is the tangent groupoid of higher order and is the complete lift of higher order of presymplectic form .
The Intersection of Four Quadrics in IP6, Abelian Surfaces and their Moduli.
The Lagrange rigid body motion
We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group with its natural...
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The Lie groupoid analogue of a symplectic Lie group
A symplectic Lie group is a Lie group with a left-invariant symplectic form. Its Lie algebra structure is that of a quasi-Frobenius Lie algebra. In this note, we identify the groupoid analogue of a symplectic Lie group. We call the aforementioned structure a -symplectic Lie groupoid; the “" is motivated by the fact that each target fiber of a -symplectic Lie groupoid is a symplectic manifold. For a Lie groupoid , we show that there is a one-to-one correspondence between quasi-Frobenius Lie algebroid...
The local Gromov-Witten invariants of configurations of rational curves.
The magnetic geodesic flow in a homogeneous field on the complex projective space.
The magnetic geodesic flow on a homogeneous symplectic manifold.
The Maxwell-Bloch equations on fractional Leibniz algebroids.
The modular class of a Poisson map
We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.
The moduli space of special lagrangian submanifolds
The -Lie property of the Jacobian as a condition for complete integrability.
The nonuniqueness of Chekanov polynomials of Legendrian knots.
The periodic Floer homology of a Dehn twist.
The quantization conjecture revisited.