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Showing 1 to 20 of 26 for “"Symplectic geometry"”.
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Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients
Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). We sh w that both are given by piecewise polynomial functions in the …
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Symplectic and complex foliations
"Symplectic (not necessarily Riemannian) foliations have a transversely symplectic structure for which many standard results of symplectic geometry have their transverse analogues: the dual bundle to the transverse bundle of a foliation is a manifold with a canonical symplectic foliation, the …
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Generically nondegenerate Poisson structures and their Lie algebroids
… as nondegenerate. This allows standard tools of symplectic geometry to be applied to concretely describe the behavior of the Poisson structure. This study encompasses various Poisson structures and Lie algebroids previously studied in the literature while also developing several new types. The …
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Folded Symplectic Toric Four -Manifolds
A folded symplectic form on an even-dimensional manifold is a closed two-form that degenerates in a suitably controlled way along a smooth hypersurface. When a torus having half the dimension of the manifold acts in a way preserving the folded symplectic form and admitting a moment map, the …
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Aspects of Generalized Geometry: Branes with Boundary, Blow-ups, Brackets and Bundles
This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a …
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Some Duality Results in Homological Algebra
… modules without recourse to linear algebra or symplectic geometry; these techniques can (when applicable) greatly improve computation time.
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Getting a handle on contact manifolds
… is analogous to that of Weinstein manifolds in symplectic geometry, with the key difference that the vector field does not necessarily have positive divergence everywhere. The surgery theory for contact manifolds contains the surgery theory for Weinstein manifolds via a sutured model for …
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Geometry of Spaces of Planar Quadrilaterals
… of this dissertation is to investigate the geometry of spaces of planar quadrilaterals. The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic geometry of these spaces …
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The sixth-order Krall differential expression and self-adjoint operators.
… by W. N. Everitt and L. Markus using complex symplectic geometry. In order to explicitly construct this self-adjoint operator, we use properties of functions in the maximal domain in L2(-1, 1) of the Krall expression. As we will see, continuity, as a boundary condition, is forced by our …
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Symplectic properties of Milnor fibres
We present two results relating to the symplectic geometry of the Milnor fibres of isolated affine hypersurface singularities. First, given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the …
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Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences
We present three different aspects of symplectic geometry in connection to complex geometry. Convex symplectic manifolds, symplectic divisors and Lagrangians are central objects to study on the symplectic side. The focus of the thesis is to establish relations of these symplectic objects to the …
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Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory
… two parts covering distinct topics in algebraic geometry. In Part I, we construct the first examples of regular del Pezzo surfaces for which the first cohomology group of the structure sheaf is nonzero. Such surfaces, which only exist over imperfect fields, arise as generic fibres of fibrations …
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Questions around symplectic capacities
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Symplectic toric stratified spaces with isolated singularities
… a classification of two types of toric objects: symplectic toric cones and symplectic toric stratified spaces with isolated singularities. Both types of object are classified via orbital moment map and a second degree cohomology class. As symplectic toric stratified spaces with isolated …
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A classification of toric, folded-symplectic manifolds
Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual of the Lie algebra of the torus, $G$. The map $\psi$ has …
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Geometric structures on the target space of Hamiltonian evolution equations
… 3 is based on [J. T. Ferguson. Flat pencils of symplectic connections and Hamiltonian operators of degree 2. J. Geom. Phys., 58(4):468–486, 2008]. It is original, except for the background material in Section 3.1. In it we explain the (almost) symplectic geometry associated to Hamiltonian …
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Toric Varieties Associated with Moduli Spaces
Any genus g surface, Σg,n with n boundary components may be given a trinion decomposition: a realization of the surface as a union of 2g – 2 + n trinions glued together along 3g – 3 + n of their boundary circles. Together with the flows of Goldman, Jeffrey and Weitsman use the trinion boundary …
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Contact geometric theory of Anosov flows in dimension three and related topics
… consists of the author's work on the contact and symplectic geometric theory of Anosov flows in low dimensions, as well as the related topics from Riemannian geometry. This includes the study of the interplay between various geometric, topological and dynamical features of such flows. After …
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The contact property for magnetic flows on surfaces
… E on the tangent bundle TM endowed with a symplectic form ω_σ, where E is the kinetic energy. Our main goal is to prove existence results for a) periodic orbits, and b) Poincare sections for motions on a fixed energy level Σ_m := {E = m^2/2} ⊂ T M . We tackle this problem by studying the …
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