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Browse Dissertations and Theses  Mathematics by Contributor "Kerman, Ely"
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(20130524)We study vortex equations with a parameter $s$ on smooth vector bundles $E$ over compact K\"ahler manifolds $M$. For each $s$, we invoke techniques in \cite{Br} by turning vortex equations into the elliptic partial ...
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(20150715)Given a $G$toric, foldedsymplectic manifold with coorientable 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 ...
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(20120206)A GKM manifold is a symplectic manifold with a torus action such that the fixed points are isolated and the isotropy weights at the fixed points are linearly independent. Each GKM manifold has a GKM graph which contains ...
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(20140916)This thesis covers four results: 1. We prove an analog of Whitney's embedding theorem for Jholomorphic discs. 2. For zj = xj + i*yj in C and let D_R^2 = {(z1, z2) in C^2 : x1^2 + x2^2 <1, y1^2 + y2^2 < 1} be the real ...
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(20120627)We utilize Floer theory and an index relation relating the Maslov index, Morse index and ConleyZehnder index for a periodic orbit of the flow of a specific Hamiltonian function to state and prove some nonexistence results ...
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(20150407)Consider a symplectic circle action on a closed symplectic manifold $M$ with nonempty isolated fixed points. Associated to each fixed point, there are welldefined nonzero integers, called \emph{weights}. We prove that ...
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(20180409)This thesis treats two main topics: calibrated symplectic foliations, and local Lie groupoids. Calibrated symplectic foliations are one possible generalization of taut foliations of 3manifolds to higher dimensions. Their ...
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(20170705)We provide 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 ...
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Now showing items 18 of 8