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.
The Quantum Birkhoff Normal Form and Spectral Asymptotics
In this talk we explain a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy . This permits a detailed study of the spectrum in various asymptotic regions of the parameters , and gives improvements and new proofs for many of the results in the field. In the completely resonant...
The reduction of the standard k-cosymplectic manifold associated to a regular lagrangian
The aim of the paper is to define a k-cosymplectic structure on the standard k-cosymplectic manifold associated to a regular Lagrangian and to reduce it via Marsden-Weinstein reduction.
The scattering problem for a noncommutative nonlinear Schrödinger equation.
The Schouten-van Kampen Affine Connections Adapted to Almost (Para)Contact Metric Structures
The space of clouds in Euclidean space.
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...