Related papers: Volume and symplectic structure for l-adic local s…

We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect…

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…

We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive,…

We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

The chiral space of local fields in Sine-Gordon or the SU(2)-invariant Thirring model is studied as a module over the commutative algebra D of local integrals of motion. Using the recent construction of form factors by means of quantum…

The optimal density function assigns to each symplectic toric manifold $M$ a number $0 < d \leq 1$ obtained by considering the ratio between the maximum volume of $M$ which can be filled by symplectically embedded disjoint balls and the…

In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs $C^\infty$ deformations of coisotropic submanifolds and define the corresponding $C^\infty$-moduli space of…

We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a $2n$-dimensional manifold. In the $\mathbb C$-analytic category this set consists of the Martinet hypersurface…

We explain the geometric origin of the $L_{\infty}$-algebra controlling deformations of pre-symplectic structures.

The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…

We propose a symplectic structure for the phase space of a generic Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The symplectic structure does not require explicit knowledge of the derivative content of the…

Let $M$ be a closed, oriented, negatively curved, $n$-dimensional manifold with fundamental group $\Gamma$. Let $S^\infty$ be the unit sphere in $\ell^2(\Gamma)$, on which $\Gamma$ acts by the regular representation. The spherical volume of…

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

In this paper, we investigate the geometries associated with 3-forms of various orbital types on a symplectic 6-manifold. We show that there are extremely rich geometric structures attached to certain unstable 3-forms arising naturally from…

Let $\Sigma_{g,n}$ be a compact oriented surface with genus $g\geq 2$ bordered by $n$ circles. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah-Bott-Goldman-Narasimhan symplectic form on the space of…

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal…

Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…

In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs $C^\infty$ deformations of coisotropic submanifolds and define the corresponding…

We develop techniques for defining and working with virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves which are not necessarily cut out transversally. Such techniques have the potential for applications as foundations…