Related papers: Weinstein neighbourhood theorems for stratified su…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…

Recently, it has become clear that neighboring multiple vacua might have interesting consequences for the physics of the early universe. In this paper we investigate the topography of the string landscape corresponding to complex structure…

We study the singularities of the isotropic skeleton of a Weinstein manifold in relation to Nadler's program of arboreal singularities. By deforming the skeleton via homotopies of the Weinstein structure, we produce a Morse-Bott*…

This is an expanded version of lectures given in Hangzhou and Beijing, on the symplectic forms common to Seiberg-Witten theory and the theory of solitons. Methods for evaluating the prepotential are discussed. The construction of new…

In this paper, we give an algorithm for describing the Weinstein presentation of Weinstein subdomains obtained by carving out regular Lagrangians. Our work generalizes previous work in dimension three and requires a novel Legendrian isotopy…

We provide a lower bound for the embedding capacity of higher-dimensional symplectic ellipsoids, formulated in terms of the Lagrangian capacity of ellipsoids. Our approach relies on examining the Borman--Sheridan class of a Weinstein…

In this paper we give an alternative proof of Schreiber's theorem which says that an infinite discrete approximate subgroup in $\mathbb{R}^d$ is relatively dense around a subspace. We also deduce from Schreiber's theorem two new results.…

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics.…

We give an proof on the Weinstein conjecture on the cotangent bundles of open manifolds. Its proof is based on Gromov's nonlinear Fredholm alternative.

We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank-one totally geodesic subspaces. Among the consequences, we prove the existence of a non-constant, globally defined…

We study generalized complex manifolds from the point of view of symplectic and Poisson geometry. We start by showing that every generalized complex manifold admits a canonical Poisson structure. We use this fact, together with Weinstein's…

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

The null splitting theorem (proved in math.DG/9909158) is discussed. As an application, a uniqueness theorem for Minkowski space and for de Sitter space associated with the occurrence of null lines (inextendible globally achronal null…

This short note provides a symplectic analogue of Vaisman's theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in…

We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient…

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…

In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…

The Schmidt's subspace theory with moving targets, as a significant branch in this field, has been substantially developed in recent years. We continue the approach of the previous work, construct a weighted version of generalized Schmidt…