subject:(Symplectic geometry)

Cornell University

1. Hoffman, Benjamin S. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.

Degree: PhD, Mathematics, 2020, Cornell University

► I present three papers written on the theme of the interaction between polyhedra and Hamil- tonian mechanics. In the first, I extend Delzant’s classification of… (more)

Subjects/Keywords: Symplectic Geometry

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APA (6^th Edition):

Hoffman, B. S. (2020). POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/70413

Chicago Manual of Style (16^th Edition):

Hoffman, Benjamin S. “POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.” 2020. Doctoral Dissertation, Cornell University. Accessed March 05, 2021. http://hdl.handle.net/1813/70413.

MLA Handbook (7^th Edition):

Hoffman, Benjamin S. “POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.” 2020. Web. 05 Mar 2021.

Vancouver:

Hoffman BS. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. [Internet] [Doctoral dissertation]. Cornell University; 2020. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1813/70413.

Council of Science Editors:

Hoffman BS. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. [Doctoral Dissertation]. Cornell University; 2020. Available from: http://hdl.handle.net/1813/70413

University of Oxford

2. Wilkins, Nicholas. Quantum Steenrod squares, related operations, and their properties.

Degree: PhD, 2018, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

► In this thesis, we generalise the Steenrod square on the cohomology of a topological space to a quantum Steenrod square on the quantum cohomology of… (more)

Subjects/Keywords: Symplectic geometry

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APA (6^th Edition):

Wilkins, N. (2018). Quantum Steenrod squares, related operations, and their properties. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

Chicago Manual of Style (16^th Edition):

Wilkins, Nicholas. “Quantum Steenrod squares, related operations, and their properties.” 2018. Doctoral Dissertation, University of Oxford. Accessed March 05, 2021. http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593.

MLA Handbook (7^th Edition):

Wilkins, Nicholas. “Quantum Steenrod squares, related operations, and their properties.” 2018. Web. 05 Mar 2021.

Vancouver:

Wilkins N. Quantum Steenrod squares, related operations, and their properties. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2021 Mar 05]. Available from: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593.

Council of Science Editors:

Wilkins N. Quantum Steenrod squares, related operations, and their properties. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

University of Illinois – Urbana-Champaign

3. Wolbert, Seth P. Symplectic toric stratified spaces with isolated singularities.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98085

► 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… (more)

▼ 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 degree cohomology class. As symplectic toric stratified spaces with isolated singularities are locally modeled on symplectic toric cones, we first focus on classifying symplectic toric cones. We show that symplectic toric cones have a certain type of map (called homogeneous unimodular local embeddings) as orbital moment maps. Conversely, every homogeneous unimodular local embedding has a symplectic toric cone for which it is an orbital moment map. We classify the symplectic toric cones with the same orbital moment map by showing that their isomorphism classes are in bijective correspondence with the first Chern classes of principal G-bundles over W. This generalizes Lerman’s classification of compact connected contact toric manifolds. Symplectic toric stratified spaces with isolated singularities are spaces with neighborhoods of singularities modeled on symplectic cones. We first show their quotients W are space stratified by manifolds with corners and their moment maps are a particular type of map called stratified unimodular local embeddings. Every stratified unimodular local embedding is the orbital moment map of a symplectic toric stratified space. Finally, we show that, for any stratified unimodular local embedding, the isomorphism classes of symplectic toric stratified spaces with isolated singularities with a given orbital moment map are in bijective correspondence with a collection of cohomology classes dependent on the topology of W. This generalizes Burns, Guillemin, and Lerman’s classification of the compact connected symplectic toric stratified spaces with isolated singularities. Advisors/Committee Members: Lerman, Eugene (advisor), Tolman, Susan (Committee Chair), Loja Fernandes, Rui (committee member), Kerman, Ely (committee member).

Subjects/Keywords: Symplectic geometry

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APA (6^th Edition):

Wolbert, S. P. (2017). Symplectic toric stratified spaces with isolated singularities. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98085

Chicago Manual of Style (16^th Edition):

Wolbert, Seth P. “Symplectic toric stratified spaces with isolated singularities.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 05, 2021. http://hdl.handle.net/2142/98085.

MLA Handbook (7^th Edition):

Wolbert, Seth P. “Symplectic toric stratified spaces with isolated singularities.” 2017. Web. 05 Mar 2021.

Vancouver:

Wolbert SP. Symplectic toric stratified spaces with isolated singularities. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2142/98085.

Council of Science Editors:

Wolbert SP. Symplectic toric stratified spaces with isolated singularities. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98085

Columbia University

4. Zhang, Zhongyi. On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold.

Degree: 2020, Columbia University

URL: https://doi.org/10.7916/d8-9xbk-hq04

► We introduce an A_∞ map from the cubical chain complex of the based loop space of Lagrangian submanifolds with Legendrian boundary in a Liouville Manifold… (more)

Subjects/Keywords: Mathematics; Symplectic geometry

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APA (6^th Edition):

Zhang, Z. (2020). On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-9xbk-hq04

Chicago Manual of Style (16^th Edition):

Zhang, Zhongyi. “On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold.” 2020. Doctoral Dissertation, Columbia University. Accessed March 05, 2021. https://doi.org/10.7916/d8-9xbk-hq04.

MLA Handbook (7^th Edition):

Zhang, Zhongyi. “On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold.” 2020. Web. 05 Mar 2021.

Vancouver:

Zhang Z. On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold. [Internet] [Doctoral dissertation]. Columbia University; 2020. [cited 2021 Mar 05]. Available from: https://doi.org/10.7916/d8-9xbk-hq04.

Council of Science Editors:

Zhang Z. On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold. [Doctoral Dissertation]. Columbia University; 2020. Available from: https://doi.org/10.7916/d8-9xbk-hq04

University of California – Berkeley

5. McMillan, Aaron Fraenkel. On Embedding Singular Poisson Spaces.

Degree: Mathematics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/6xz306q4

► This dissertation investigates the problem of locally embedding singular Poisson spaces. Specifically, it seeks to understand when a singular symplectic quotient V/G of a symplectic… (more)

Subjects/Keywords: Mathematics; Poisson geometry; Symplectic geometry

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APA (6^th Edition):

McMillan, A. F. (2011). On Embedding Singular Poisson Spaces. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/6xz306q4

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

McMillan, Aaron Fraenkel. “On Embedding Singular Poisson Spaces.” 2011. Thesis, University of California – Berkeley. Accessed March 05, 2021. http://www.escholarship.org/uc/item/6xz306q4.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

McMillan, Aaron Fraenkel. “On Embedding Singular Poisson Spaces.” 2011. Web. 05 Mar 2021.

Vancouver:

McMillan AF. On Embedding Singular Poisson Spaces. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2021 Mar 05]. Available from: http://www.escholarship.org/uc/item/6xz306q4.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McMillan AF. On Embedding Singular Poisson Spaces. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/6xz306q4

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Rochester

6. Cho, Hyunjoo. Existence of almost contact structures on manifolds with G2-structures and generalizations.

Degree: PhD, 2012, University of Rochester

URL: http://hdl.handle.net/1802/21273

► This dissertation consists of two main results. First, we investigate the relationship between almost contact structures and G2-structures on seven-dimensional Riemannian manifolds: we show that… (more)

Subjects/Keywords: Differential geometry; Symplectic geometry

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APA (6^th Edition):

Cho, H. (2012). Existence of almost contact structures on manifolds with G2-structures and generalizations. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/21273

Chicago Manual of Style (16^th Edition):

Cho, Hyunjoo. “Existence of almost contact structures on manifolds with G2-structures and generalizations.” 2012. Doctoral Dissertation, University of Rochester. Accessed March 05, 2021. http://hdl.handle.net/1802/21273.

MLA Handbook (7^th Edition):

Cho, Hyunjoo. “Existence of almost contact structures on manifolds with G2-structures and generalizations.” 2012. Web. 05 Mar 2021.

Vancouver:

Cho H. Existence of almost contact structures on manifolds with G2-structures and generalizations. [Internet] [Doctoral dissertation]. University of Rochester; 2012. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1802/21273.

Council of Science Editors:

Cho H. Existence of almost contact structures on manifolds with G2-structures and generalizations. [Doctoral Dissertation]. University of Rochester; 2012. Available from: http://hdl.handle.net/1802/21273

University of Toronto

7. Uren, James. Toric Varieties Associated with Moduli Spaces.

Degree: 2011, University of Toronto

URL: http://hdl.handle.net/1807/31960

►

Any genus g surface, Σ_g,n, with n boundary components may be given a trinion decomposition: a realization of the surface as a union of 2g-2+n… (more)

Subjects/Keywords: Symplectic Geometry; Toric Geometry; 0405

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APA (6^th Edition):

Uren, J. (2011). Toric Varieties Associated with Moduli Spaces. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/31960

Chicago Manual of Style (16^th Edition):

Uren, James. “Toric Varieties Associated with Moduli Spaces.” 2011. Doctoral Dissertation, University of Toronto. Accessed March 05, 2021. http://hdl.handle.net/1807/31960.

MLA Handbook (7^th Edition):

Uren, James. “Toric Varieties Associated with Moduli Spaces.” 2011. Web. 05 Mar 2021.

Vancouver:

Uren J. Toric Varieties Associated with Moduli Spaces. [Internet] [Doctoral dissertation]. University of Toronto; 2011. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1807/31960.

Council of Science Editors:

Uren J. Toric Varieties Associated with Moduli Spaces. [Doctoral Dissertation]. University of Toronto; 2011. Available from: http://hdl.handle.net/1807/31960

Columbia University

8. Zhao, Jingyu. Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions.

Degree: 2016, Columbia University

URL: https://doi.org/10.7916/D8V69JMZ

► Given a Liouville manifold, symplectic cohomology is defined as the Hamiltonian Floer homology for the symplectic action functional on the free loop space. In this… (more)

Subjects/Keywords: Symplectic geometry; Homology theory; Mathematics

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APA (6^th Edition):

Zhao, J. (2016). Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8V69JMZ

Chicago Manual of Style (16^th Edition):

Zhao, Jingyu. “Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions.” 2016. Doctoral Dissertation, Columbia University. Accessed March 05, 2021. https://doi.org/10.7916/D8V69JMZ.

MLA Handbook (7^th Edition):

Zhao, Jingyu. “Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions.” 2016. Web. 05 Mar 2021.

Vancouver:

Zhao J. Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions. [Internet] [Doctoral dissertation]. Columbia University; 2016. [cited 2021 Mar 05]. Available from: https://doi.org/10.7916/D8V69JMZ.

Council of Science Editors:

Zhao J. Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions. [Doctoral Dissertation]. Columbia University; 2016. Available from: https://doi.org/10.7916/D8V69JMZ

University of Toronto

9. Luk, Kevin. Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry.

Degree: 2012, University of Toronto

URL: http://hdl.handle.net/1807/33298

►

The following is my M.Sc. thesis on moduli space techniques in algebraic and symplectic geometry. It is divided into the following two parts: the rst… (more)

Subjects/Keywords: Pure Mathematics; Algebraic Geometry; Symplectic Geometry; 0405

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APA (6^th Edition):

Luk, K. (2012). Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/33298

Chicago Manual of Style (16^th Edition):

Luk, Kevin. “Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry.” 2012. Masters Thesis, University of Toronto. Accessed March 05, 2021. http://hdl.handle.net/1807/33298.

MLA Handbook (7^th Edition):

Luk, Kevin. “Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry.” 2012. Web. 05 Mar 2021.

Vancouver:

Luk K. Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry. [Internet] [Masters thesis]. University of Toronto; 2012. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1807/33298.

Council of Science Editors:

Luk K. Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry. [Masters Thesis]. University of Toronto; 2012. Available from: http://hdl.handle.net/1807/33298

Uppsala University

10. Iakovidis, Nikolaos. Geometry of Contact Toric Manifolds in 3D.

Degree: Theoretical Physics, 2016, Uppsala University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296221

► In this project we present some applications of symplectic and contact geometry on 3-manifolds. In the first section we introduce the notion of symplectic… (more)

Subjects/Keywords: Symplectic Geometry; Contact Geometry; Lens spaces

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APA (6^th Edition):

Iakovidis, N. (2016). Geometry of Contact Toric Manifolds in 3D. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296221

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Iakovidis, Nikolaos. “Geometry of Contact Toric Manifolds in 3D.” 2016. Thesis, Uppsala University. Accessed March 05, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296221.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Iakovidis, Nikolaos. “Geometry of Contact Toric Manifolds in 3D.” 2016. Web. 05 Mar 2021.

Vancouver:

Iakovidis N. Geometry of Contact Toric Manifolds in 3D. [Internet] [Thesis]. Uppsala University; 2016. [cited 2021 Mar 05]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296221.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Iakovidis N. Geometry of Contact Toric Manifolds in 3D. [Thesis]. Uppsala University; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296221

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

11. Lambert-Cole, Peter. Invariants of Legendrian products.

Degree: PhD, Applied Mathematics, 2014, Louisiana State University

URL: etd-07142014-122759 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2909

This thesis investigates a construction in contact topology of Legendrian submanifolds called the Legendrian product. We investigate and compute invariants for these Legendrian submanifolds, including the Thurston-Bennequin invariant and Maslov class; Legendrian contact homology for the product of two Legendrian knots; and generating family homology.

Subjects/Keywords: low-dimensional topology; Contact geometry; symplectic geometry

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APA (6^th Edition):

Lambert-Cole, P. (2014). Invariants of Legendrian products. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07142014-122759 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2909

Chicago Manual of Style (16^th Edition):

Lambert-Cole, Peter. “Invariants of Legendrian products.” 2014. Doctoral Dissertation, Louisiana State University. Accessed March 05, 2021. etd-07142014-122759 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2909.

MLA Handbook (7^th Edition):

Lambert-Cole, Peter. “Invariants of Legendrian products.” 2014. Web. 05 Mar 2021.

Vancouver:

Lambert-Cole P. Invariants of Legendrian products. [Internet] [Doctoral dissertation]. Louisiana State University; 2014. [cited 2021 Mar 05]. Available from: etd-07142014-122759 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2909.

Council of Science Editors:

Lambert-Cole P. Invariants of Legendrian products. [Doctoral Dissertation]. Louisiana State University; 2014. Available from: etd-07142014-122759 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2909

University of Cambridge

12. Kirchhoff-Lukat, Charlotte Sophie. Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles.

Degree: PhD, 2018, University of Cambridge

URL: https://doi.org/10.17863/CAM.30372 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763570

► 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… (more)

▼ 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 correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.

Subjects/Keywords: 516.3; differential geometry; generalized complex geometry; Poisson geometry; symplectic geometry

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APA (6^th Edition):

Kirchhoff-Lukat, C. S. (2018). Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.30372 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763570

Chicago Manual of Style (16^th Edition):

Kirchhoff-Lukat, Charlotte Sophie. “Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles.” 2018. Doctoral Dissertation, University of Cambridge. Accessed March 05, 2021. https://doi.org/10.17863/CAM.30372 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763570.

MLA Handbook (7^th Edition):

Kirchhoff-Lukat, Charlotte Sophie. “Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles.” 2018. Web. 05 Mar 2021.

Vancouver:

Kirchhoff-Lukat CS. Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles. [Internet] [Doctoral dissertation]. University of Cambridge; 2018. [cited 2021 Mar 05]. Available from: https://doi.org/10.17863/CAM.30372 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763570.

Council of Science Editors:

Kirchhoff-Lukat CS. Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles. [Doctoral Dissertation]. University of Cambridge; 2018. Available from: https://doi.org/10.17863/CAM.30372 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763570

Cornell University

13. Pendleton, Ian Alexander. The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds.

Degree: PhD, Mathematics, 2019, Cornell University

URL: http://hdl.handle.net/1813/67332

► This is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of… (more)

Subjects/Keywords: algebraic topology; toric origami; toric symplectic; Mathematics; symplectic geometry

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APA (6^th Edition):

Pendleton, I. A. (2019). The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/67332

Chicago Manual of Style (16^th Edition):

Pendleton, Ian Alexander. “The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds.” 2019. Doctoral Dissertation, Cornell University. Accessed March 05, 2021. http://hdl.handle.net/1813/67332.

MLA Handbook (7^th Edition):

Pendleton, Ian Alexander. “The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds.” 2019. Web. 05 Mar 2021.

Vancouver:

Pendleton IA. The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds. [Internet] [Doctoral dissertation]. Cornell University; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1813/67332.

Council of Science Editors:

Pendleton IA. The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds. [Doctoral Dissertation]. Cornell University; 2019. Available from: http://hdl.handle.net/1813/67332

University of Colorado

14. Nita, Alexander. Essential Self-Adjointness of the Symplectic Dirac Operators.

Degree: PhD, Mathematics, 2016, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/45

► The main problem we consider in this thesis is the essential self-adjointness of the symplectic Dirac operators D and ~D constructed by Katharina Habermann… (more)

Subjects/Keywords: Dirac operator; functional analysis; self-adjointness; symplectic geometry; symplectic topology; Mathematics

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APA (6^th Edition):

Nita, A. (2016). Essential Self-Adjointness of the Symplectic Dirac Operators. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/45

Chicago Manual of Style (16^th Edition):

Nita, Alexander. “Essential Self-Adjointness of the Symplectic Dirac Operators.” 2016. Doctoral Dissertation, University of Colorado. Accessed March 05, 2021. https://scholar.colorado.edu/math_gradetds/45.

MLA Handbook (7^th Edition):

Nita, Alexander. “Essential Self-Adjointness of the Symplectic Dirac Operators.” 2016. Web. 05 Mar 2021.

Vancouver:

Nita A. Essential Self-Adjointness of the Symplectic Dirac Operators. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Mar 05]. Available from: https://scholar.colorado.edu/math_gradetds/45.

Council of Science Editors:

Nita A. Essential Self-Adjointness of the Symplectic Dirac Operators. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/math_gradetds/45

University of Minnesota

15. Mak, Cheuk Yu. Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences.

Degree: PhD, Mathematics, 2016, University of Minnesota

URL: http://hdl.handle.net/11299/182326

► 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… (more)

Subjects/Keywords: Dehn twists; Log Calabi-Yau surfaces; Symplectic fillings; Symplectic geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mak, C. Y. (2016). Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/182326

Chicago Manual of Style (16^th Edition):

Mak, Cheuk Yu. “Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences.” 2016. Doctoral Dissertation, University of Minnesota. Accessed March 05, 2021. http://hdl.handle.net/11299/182326.

MLA Handbook (7^th Edition):

Mak, Cheuk Yu. “Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences.” 2016. Web. 05 Mar 2021.

Vancouver:

Mak CY. Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences. [Internet] [Doctoral dissertation]. University of Minnesota; 2016. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/11299/182326.

Council of Science Editors:

Mak CY. Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences. [Doctoral Dissertation]. University of Minnesota; 2016. Available from: http://hdl.handle.net/11299/182326

University of Georgia

16. Needham, Thomas Richard. Grassmannian geometry of framed curve spaces.

Degree: 2016, University of Georgia

URL: http://hdl.handle.net/10724/36282

► We develop a general framework for solving a variety of variational and computer vision problems involving framed space curves. Our approach is to study the… (more)

Subjects/Keywords: Infinite-dimensional geometry; symplectic geometry; Riemannian geometry; elastic shape matching

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Needham, T. R. (2016). Grassmannian geometry of framed curve spaces. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/36282

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Needham, Thomas Richard. “Grassmannian geometry of framed curve spaces.” 2016. Thesis, University of Georgia. Accessed March 05, 2021. http://hdl.handle.net/10724/36282.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Needham, Thomas Richard. “Grassmannian geometry of framed curve spaces.” 2016. Web. 05 Mar 2021.

Vancouver:

Needham TR. Grassmannian geometry of framed curve spaces. [Internet] [Thesis]. University of Georgia; 2016. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10724/36282.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Needham TR. Grassmannian geometry of framed curve spaces. [Thesis]. University of Georgia; 2016. Available from: http://hdl.handle.net/10724/36282

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Cambridge

17. Benedetti, Gabriele. The contact property for magnetic flows on surfaces.

Degree: PhD, 2015, University of Cambridge

URL: https://doi.org/10.17863/CAM.16235 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642462

► This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is… (more)

▼ This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical systems are described by the Hamiltonian equations of a function 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 = m²/2} ⊂ T M . We tackle this problem by studying the contact geometry of the level set Σ_m . This will allow us to a) count periodic orbits using algebraic invariants such as the Symplectic Cohomology SH of the sublevels ({E ≤ m²/2}, ω_σ ); b) find Poincare sections starting from pseudo-holomorphic foliations, using the techniques developed by Hofer, Wysocki and Zehnder in 1998. In Chapter 3 we give a proof of the invariance of SH under deformation in an abstract setting, suitable for the applications. In Chapter 4 we present some new results on the energy values of contact type. First, we give explicit examples of exact magnetic systems on T² which are of contact type at the strict critical value. Then, we analyse the case of non-exact systems on M different from T² and prove that, for large m and for small m with symplectic σ, Σ_m is of contact type. Finally, we compute SH in all cases where Σ_m is convex. On the other hand, we are also interested in non-exact examples where the contact property fails. While for surfaces of genus at least two, there is always a level not of contact type for topological reasons, this is not true anymore for S² . In Chapter 5, after developing the theory of magnetic flows on surfaces of revolution, we exhibit the first example on S² of an energy level not of contact type. We also give a numerical algorithm to check the contact property when the level has positive magnetic curvature. In Chapter 7 we restrict the attention to low energy levels on S² with a symplectic σ and we show that these levels are of dynamically convex contact type. Hence, we prove that, in the non-degenerate case, there exists a Poincare section of disc-type and at least an elliptic periodic orbit. In the general case, we show that there are either 2 or infinitely many periodic orbits on Σ_m and that we can divide the periodic orbits in two distinguished classes, short and long, depending on their period. Then, we look at the case of surfaces of revolution, where we give a sufficient condition for the existence of infinitely many periodic orbits. Finally, we discuss a generalisation of dynamical convexity introduced recently by Abreu and Macarini, which applies also to surfaces with genus at least two.

Subjects/Keywords: 516.3; Magnetic flows; Symplectic geometry; Periodic orbits

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Benedetti, G. (2015). The contact property for magnetic flows on surfaces. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.16235 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642462

Chicago Manual of Style (16^th Edition):

Benedetti, Gabriele. “The contact property for magnetic flows on surfaces.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 05, 2021. https://doi.org/10.17863/CAM.16235 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642462.

MLA Handbook (7^th Edition):

Benedetti, Gabriele. “The contact property for magnetic flows on surfaces.” 2015. Web. 05 Mar 2021.

Vancouver:

Benedetti G. The contact property for magnetic flows on surfaces. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 05]. Available from: https://doi.org/10.17863/CAM.16235 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642462.

Council of Science Editors:

Benedetti G. The contact property for magnetic flows on surfaces. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://doi.org/10.17863/CAM.16235 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642462

University of Cambridge

18. Benedetti, Gabriele. The contact property for magnetic flows on surfaces.

Degree: PhD, 2015, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/247157https://www.repository.cam.ac.uk/bitstream/1810/247157/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/5/thesis_Benedetti.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/6/thesis_Benedetti.pdf.jpg

► This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is… (more)

▼ This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical systems are described by the Hamiltonian equations of a function 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 = m²/2} ⊂ T M . We tackle this problem by studying the contact geometry of the level set Σ_m . This will allow us to a) count periodic orbits using algebraic invariants such as the Symplectic Cohomology SH of the sublevels ({E ≤ m²/2}, ω_σ ); b) find Poincare sections starting from pseudo-holomorphic foliations, using the techniques developed by Hofer, Wysocki and Zehnder in 1998. In Chapter 3 we give a proof of the invariance of SH under deformation in an abstract setting, suitable for the applications. In Chapter 4 we present some new results on the energy values of contact type. First, we give explicit examples of exact magnetic systems on T² which are of contact type at the strict critical value. Then, we analyse the case of non-exact systems on M different from T² and prove that, for large m and for small m with symplectic σ, Σ_m is of contact type. Finally, we compute SH in all cases where Σ_m is convex. On the other hand, we are also interested in non-exact examples where the contact property fails. While for surfaces of genus at least two, there is always a level not of contact type for topological reasons, this is not true anymore for S² . In Chapter 5, after developing the theory of magnetic flows on surfaces of revolution, we exhibit the first example on S² of an energy level not of contact type. We also give a numerical algorithm to check the contact property when the level has positive magnetic curvature. In Chapter 7 we restrict the attention to low energy levels on S² with a symplectic σ and we show that these levels are of dynamically convex contact type. Hence, we prove that, in the non-degenerate case, there exists a Poincare section of disc-type and at least an elliptic periodic orbit. In the general case, we show that there are either 2 or infinitely many periodic orbits on Σ_m and that we can divide the periodic orbits in two distinguished classes, short and long, depending on their period. Then, we look at the case of surfaces of revolution, where we give a sufficient condition for the existence of infinitely many periodic orbits. Finally, we discuss a generalisation of dynamical convexity introduced recently by Abreu and Macarini, which applies also to surfaces with genus at least two.

Subjects/Keywords: Magnetic flows; Symplectic geometry; Periodic orbits

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Benedetti, G. (2015). The contact property for magnetic flows on surfaces. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/247157https://www.repository.cam.ac.uk/bitstream/1810/247157/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/5/thesis_Benedetti.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/6/thesis_Benedetti.pdf.jpg

Chicago Manual of Style (16^th Edition):

Benedetti, Gabriele. “The contact property for magnetic flows on surfaces.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 05, 2021. https://www.repository.cam.ac.uk/handle/1810/247157https://www.repository.cam.ac.uk/bitstream/1810/247157/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/5/thesis_Benedetti.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/6/thesis_Benedetti.pdf.jpg.

MLA Handbook (7^th Edition):

Benedetti, Gabriele. “The contact property for magnetic flows on surfaces.” 2015. Web. 05 Mar 2021.

Vancouver:

Benedetti G. The contact property for magnetic flows on surfaces. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 05]. Available from: https://www.repository.cam.ac.uk/handle/1810/247157https://www.repository.cam.ac.uk/bitstream/1810/247157/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/5/thesis_Benedetti.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/6/thesis_Benedetti.pdf.jpg.

Council of Science Editors:

Benedetti G. The contact property for magnetic flows on surfaces. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://www.repository.cam.ac.uk/handle/1810/247157https://www.repository.cam.ac.uk/bitstream/1810/247157/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/5/thesis_Benedetti.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/247157/6/thesis_Benedetti.pdf.jpg

University of Oklahoma

19. Sunkula, Mahesh. GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/321110

► Quantization of a classical mechanical system is an old problem in physics. In classical mechanics, the evolution of the system is given by a Hamiltonian… (more)

Subjects/Keywords: Geometric Quantization; Symplectic Geometry; Mathematical Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sunkula, M. (2019). GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/321110

Chicago Manual of Style (16^th Edition):

Sunkula, Mahesh. “GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed March 05, 2021. http://hdl.handle.net/11244/321110.

MLA Handbook (7^th Edition):

Sunkula, Mahesh. “GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.” 2019. Web. 05 Mar 2021.

Vancouver:

Sunkula M. GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/11244/321110.

Council of Science Editors:

Sunkula M. GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/321110

University of Southern California

20. Avdek, Russell. Contact surgery, open books, and symplectic cobordisms.

Degree: PhD, Mathematics, 2013, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/304150/rec/1614

► In this thesis, we study contact manifolds and symplectic cobordisms between them using open book decompositions and various types of symplectic handle attachment. In the… (more)

Subjects/Keywords: contact geometry; symplectic geometry; contact surgery; Weinstein handle; symplectic cobordism; open book; monodromy; Dehn twist

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APA (6^th Edition):

Avdek, R. (2013). Contact surgery, open books, and symplectic cobordisms. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/304150/rec/1614

Chicago Manual of Style (16^th Edition):

Avdek, Russell. “Contact surgery, open books, and symplectic cobordisms.” 2013. Doctoral Dissertation, University of Southern California. Accessed March 05, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/304150/rec/1614.

MLA Handbook (7^th Edition):

Avdek, Russell. “Contact surgery, open books, and symplectic cobordisms.” 2013. Web. 05 Mar 2021.

Vancouver:

Avdek R. Contact surgery, open books, and symplectic cobordisms. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Mar 05]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/304150/rec/1614.

Council of Science Editors:

Avdek R. Contact surgery, open books, and symplectic cobordisms. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/304150/rec/1614

Universiteit Utrecht

21. Tel, A.W. Lefschetz fibrations and symplectic structures.

Degree: 2015, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/311281

► In this thesis, we study a relation between symplectic structures and Lefschetz ?brations to shed some light on 4-manifold theory. We introduce symplectic manifolds and… (more)

Subjects/Keywords: Lefschetz fibration; Lefschetz pencil; symplectic geometry; fiber bundle; complex geometry; compatibility

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tel, A. W. (2015). Lefschetz fibrations and symplectic structures. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/311281

Chicago Manual of Style (16^th Edition):

Tel, A W. “Lefschetz fibrations and symplectic structures.” 2015. Masters Thesis, Universiteit Utrecht. Accessed March 05, 2021. http://dspace.library.uu.nl:8080/handle/1874/311281.

MLA Handbook (7^th Edition):

Tel, A W. “Lefschetz fibrations and symplectic structures.” 2015. Web. 05 Mar 2021.

Vancouver:

Tel AW. Lefschetz fibrations and symplectic structures. [Internet] [Masters thesis]. Universiteit Utrecht; 2015. [cited 2021 Mar 05]. Available from: http://dspace.library.uu.nl:8080/handle/1874/311281.

Council of Science Editors:

Tel AW. Lefschetz fibrations and symplectic structures. [Masters Thesis]. Universiteit Utrecht; 2015. Available from: http://dspace.library.uu.nl:8080/handle/1874/311281

University of California – Berkeley

22. Canez, Santiago Valencia. Double Groupoids, Orbifolds, and the Symplectic Category.

Degree: Mathematics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/7df5f00t

► Motivated by an attempt to better understand the notion of a symplectic stack, we introduce the notion of a \emph{symplectic hopfoid}, which should be thought… (more)

Subjects/Keywords: Mathematics; category theory; differential geometry; groupoids; orbifolds; stacks; symplectic geometry

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APA (6^th Edition):

Canez, S. V. (2011). Double Groupoids, Orbifolds, and the Symplectic Category. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7df5f00t

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Canez, Santiago Valencia. “Double Groupoids, Orbifolds, and the Symplectic Category.” 2011. Thesis, University of California – Berkeley. Accessed March 05, 2021. http://www.escholarship.org/uc/item/7df5f00t.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Canez, Santiago Valencia. “Double Groupoids, Orbifolds, and the Symplectic Category.” 2011. Web. 05 Mar 2021.

Vancouver:

Canez SV. Double Groupoids, Orbifolds, and the Symplectic Category. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2021 Mar 05]. Available from: http://www.escholarship.org/uc/item/7df5f00t.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Canez SV. Double Groupoids, Orbifolds, and the Symplectic Category. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/7df5f00t

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

23. Brown, Jeffrey Steven. Gromov – Witten Invariants of Toric Fibrations.

Degree: Mathematics, 2009, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/38b8b8q5

► We prove a conjecture of Artur Elezi in a generalized form suggested by Givental. Namely, our main result relates genus-0 Gromov – Witten invariants of a… (more)

Subjects/Keywords: Mathematics; Gromov – Witten Invariant; Symplectic Geometry; Algebraic Geometry

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APA (6^th Edition):

Brown, J. S. (2009). Gromov – Witten Invariants of Toric Fibrations. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/38b8b8q5

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Brown, Jeffrey Steven. “Gromov – Witten Invariants of Toric Fibrations.” 2009. Thesis, University of California – Berkeley. Accessed March 05, 2021. http://www.escholarship.org/uc/item/38b8b8q5.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Brown, Jeffrey Steven. “Gromov – Witten Invariants of Toric Fibrations.” 2009. Web. 05 Mar 2021.

Vancouver:

Brown JS. Gromov – Witten Invariants of Toric Fibrations. [Internet] [Thesis]. University of California – Berkeley; 2009. [cited 2021 Mar 05]. Available from: http://www.escholarship.org/uc/item/38b8b8q5.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brown JS. Gromov – Witten Invariants of Toric Fibrations. [Thesis]. University of California – Berkeley; 2009. Available from: http://www.escholarship.org/uc/item/38b8b8q5

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Michigan

24. Irvine, Daniel. Symplectic Embeddings of Toric Domains.

Degree: PhD, Mathematics, 2020, University of Michigan

URL: http://hdl.handle.net/2027.42/155101

► This work examines a special class of symplectic manifolds known as toric domains. The main problem under consideration is embedding one toric domain into another… (more)

▼ This work examines a special class of symplectic manifolds known as toric domains. The main problem under consideration is embedding one toric domain into another in a way that preserves the symplectic structure. The problem of when a symplectic embedding exists is largely open, except for simple manifolds. One important example manifold, which is also a toric domain, is the symplectic polydisc, which is a product of 2-dimensional discs. We say that a polydisc is stabilized when it is crossed with several copies of the complex plane (which can be viewed as a disc of infinite radius). The main result of this work is a characterization of when a large class of stabilized polydiscs embed into other stabilized polydiscs. This result incorporates high-dimensional polydisc embeddings. In examining these stabilized polydisc embeddings we consider J -holomorphic curves, which are solutions to a PDE. A crucial step in the proof of the embedding result will be constructing J-holomorphic curves with specific boundary conditions. It turns out that the curves constructed for this theorem persist under the process of stabilizing. This makes such curves very useful for obstructing other stabilized embedding problems, which gives an avenue for future research. The 4-dimensional symplectic embedding problem can be studied quantitatively using weight vectors. Heuristically, a weight vector represents the radii of an optimal packing of symplectic balls into a toric domain, and this optimal ball packing will be described algorithmically in this work. Conversely, if one is given a weight vector, one can use this algorithm to generate a toric domain having the given vector as its weight vector. We also discuss how to pass between two classes of toric domains, called concave and convex, and examine the effect that this transformation has on weight vectors. Weight vectors are useful because they serve as a shorthand for an infinite sequence of symplectic capacities known as ECH capacities, but the computation of ECH capacities from a weight vector is difficult. Another main result of this work gives a method of simplifying weight vectors to make the computation of the corresponding ECH capacity sequence easier. Advisors/Committee Members: Burns Jr, Daniel M (committee member), Schotland, John Carl (committee member), Bloch, Anthony M (committee member), Li, Jun (committee member), Uribe-Ahumada, Alejandro (committee member).

Subjects/Keywords: differential geometry; symplectic geometry; classical mechanics; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Irvine, D. (2020). Symplectic Embeddings of Toric Domains. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/155101

Chicago Manual of Style (16^th Edition):

Irvine, Daniel. “Symplectic Embeddings of Toric Domains.” 2020. Doctoral Dissertation, University of Michigan. Accessed March 05, 2021. http://hdl.handle.net/2027.42/155101.

MLA Handbook (7^th Edition):

Irvine, Daniel. “Symplectic Embeddings of Toric Domains.” 2020. Web. 05 Mar 2021.

Vancouver:

Irvine D. Symplectic Embeddings of Toric Domains. [Internet] [Doctoral dissertation]. University of Michigan; 2020. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2027.42/155101.

Council of Science Editors:

Irvine D. Symplectic Embeddings of Toric Domains. [Doctoral Dissertation]. University of Michigan; 2020. Available from: http://hdl.handle.net/2027.42/155101

25. Lanius, Melinda Dawn. Generically nondegenerate Poisson structures and their Lie algebroids.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101536

► In this dissertation, generically nondegenerate Poisson manifolds are studied by lifting them to a Lie algebroid where they can be understood as nondegenerate. This allows… (more)

Subjects/Keywords: Poisson geometry; symplectic geometry

…1.1 Poisson and symplectic geometry A Poisson manifold (M, π) is a manifold M… …tools of symplectic geometry to the Lie algebroid. Moser. We use the standard Moser… …which we have hope of applying standard techniques of symplectic geometry. 2.2.1 Lie… …hypersurfaces), we can adapt the standard Moser technique of symplectic geometry to establish… …a symplectic one and allow us to view the Poisson structure as non-degenerate. The second…

10 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lanius, M. D. (2018). Generically nondegenerate Poisson structures and their Lie algebroids. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101536

Chicago Manual of Style (16^th Edition):

Lanius, Melinda Dawn. “Generically nondegenerate Poisson structures and their Lie algebroids.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 05, 2021. http://hdl.handle.net/2142/101536.

MLA Handbook (7^th Edition):

Lanius, Melinda Dawn. “Generically nondegenerate Poisson structures and their Lie algebroids.” 2018. Web. 05 Mar 2021.

Vancouver:

Lanius MD. Generically nondegenerate Poisson structures and their Lie algebroids. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2142/101536.

Council of Science Editors:

Lanius MD. Generically nondegenerate Poisson structures and their Lie algebroids. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101536

University of Toronto

26. Bischoff, Francis Rene Losier. Morita Equivalence and Generalized Kähler Geometry.

Degree: PhD, 2019, University of Toronto

URL: http://hdl.handle.net/1807/97318

► Generalized Kähler (GK) geometry is a generalization of Kähler geometry, which arises in the study of supersymmetric sigma models in physics. In this thesis, we… (more)

Subjects/Keywords: Generalized Kähler geometry; Morita equivalence; Poisson geometry; Symplectic groupoid; 0405

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bischoff, F. R. L. (2019). Morita Equivalence and Generalized Kähler Geometry. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/97318

Chicago Manual of Style (16^th Edition):

Bischoff, Francis Rene Losier. “Morita Equivalence and Generalized Kähler Geometry.” 2019. Doctoral Dissertation, University of Toronto. Accessed March 05, 2021. http://hdl.handle.net/1807/97318.

MLA Handbook (7^th Edition):

Bischoff, Francis Rene Losier. “Morita Equivalence and Generalized Kähler Geometry.” 2019. Web. 05 Mar 2021.

Vancouver:

Bischoff FRL. Morita Equivalence and Generalized Kähler Geometry. [Internet] [Doctoral dissertation]. University of Toronto; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1807/97318.

Council of Science Editors:

Bischoff FRL. Morita Equivalence and Generalized Kähler Geometry. [Doctoral Dissertation]. University of Toronto; 2019. Available from: http://hdl.handle.net/1807/97318

Cornell University

27. Huynh, My Thanh. The Gromov Width of Symplectic Cuts of Symplectic Manifolds.

Degree: PhD, Mathematics, 2018, Cornell University

URL: http://hdl.handle.net/1813/59394

► In 1985, Gromov discovered a rigidity phenonmenon for symplectic embeddings which led to the concept of Gromov width: a measure of the largest ball that… (more)

Subjects/Keywords: grassmannian; gromov width; pseudoholomorphic curves; symplectic cut; symplectic geometry; toric variety; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Huynh, M. T. (2018). The Gromov Width of Symplectic Cuts of Symplectic Manifolds. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/59394

Chicago Manual of Style (16^th Edition):

Huynh, My Thanh. “The Gromov Width of Symplectic Cuts of Symplectic Manifolds.” 2018. Doctoral Dissertation, Cornell University. Accessed March 05, 2021. http://hdl.handle.net/1813/59394.

MLA Handbook (7^th Edition):

Huynh, My Thanh. “The Gromov Width of Symplectic Cuts of Symplectic Manifolds.” 2018. Web. 05 Mar 2021.

Vancouver:

Huynh MT. The Gromov Width of Symplectic Cuts of Symplectic Manifolds. [Internet] [Doctoral dissertation]. Cornell University; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1813/59394.

Council of Science Editors:

Huynh MT. The Gromov Width of Symplectic Cuts of Symplectic Manifolds. [Doctoral Dissertation]. Cornell University; 2018. Available from: http://hdl.handle.net/1813/59394

Université Catholique de Louvain

28. Voglaire, Yannick. Quantization of solvable symplectic symmetric spaces.

Degree: 2011, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/106799

►

Geometry and physics have a long history of mutual interactions. Among those interactions coming from quantum mechanics, the early “Weyl quantization” of the phase space… (more)

▼

Geometry and physics have a long history of mutual interactions. Among those interactions coming from quantum mechanics, the early “Weyl quantization” of the phase space observables paved the way for the understanding of some deep relations between Poisson geometry and quantum algebras. As two outgrowths, of prime importance in the last decades were the Moyal and Weyl products, respectively in formal and non-formal deformation quantization. The notion of a midpoint of two given points appears naturally in the Weyl quantization and product, suggesting to consider symplectic symmetric spaces with midpoint map. A basic conjecture of Weinstein in this context relates the associativity of non-formal products of functions with the symplectic area of so-called “double triangles”. The aim of this thesis is to improve the understanding of the structure of solvable symplectic symmetric spaces and to provide the necessary tools for an inductive construction of quantizations of these spaces satisfying the above conjecture. For a general symmetric space, we relate the existence of a midpoint map to the existence and uniqueness of geodesics joining two points, and characterize the symmetric spaces for which each triangle has a unique double triangle. We introduce symplectic reduction and double extension for symplectic symmetric spaces, and uncover a “primitive structure” canonically attached to any such space, allowing the construction of T-star extensions à la Bordemann. We then study the behaviour of the main ingredient in our proposed quantization procedure, the Severa projection, under the above-mentioned operations. We end the thesis by providing explicit computations for a new class of examples yielding in particular new universal deformation formulæ for the actions of some symplectic Lie groups on Fréchet algebras.

(MATH 3) – UCL, 2011

Advisors/Committee Members: UCL - SST/IRMP/IRMP - Institut de recherche en mathématique et physique, Bieliavsky, Pierre, Pevzner, Michael, Félix, Yves, Gayral, Victor, Maeda, Yoshiaki, Xu, Ping.

Subjects/Keywords: Quantization; Symplectic geometry; Symmetric spaces; Lie theory; Symplectic reduction; Double extension; Midpoint map

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Voglaire, Y. (2011). Quantization of solvable symplectic symmetric spaces. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/106799

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Voglaire, Yannick. “Quantization of solvable symplectic symmetric spaces.” 2011. Thesis, Université Catholique de Louvain. Accessed March 05, 2021. http://hdl.handle.net/2078.1/106799.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Voglaire, Yannick. “Quantization of solvable symplectic symmetric spaces.” 2011. Web. 05 Mar 2021.

Vancouver:

Voglaire Y. Quantization of solvable symplectic symmetric spaces. [Internet] [Thesis]. Université Catholique de Louvain; 2011. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2078.1/106799.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Voglaire Y. Quantization of solvable symplectic symmetric spaces. [Thesis]. Université Catholique de Louvain; 2011. Available from: http://hdl.handle.net/2078.1/106799

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

29. Eddy, Thomas D. Improved stick number upper bounds.

Degree: MS(M.S.), Mathematics, 2019, Colorado State University

URL: http://hdl.handle.net/10217/195411

► A stick knot is a mathematical knot formed by a chain of straight line segments. For a knot K, define the stick number of K,… (more)

Subjects/Keywords: knot theory; stick number; toric symplectic manifold; polygon index; edge number; symplectic geometry

10 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Eddy, T. D. (2019). Improved stick number upper bounds. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/195411

Chicago Manual of Style (16^th Edition):

Eddy, Thomas D. “Improved stick number upper bounds.” 2019. Masters Thesis, Colorado State University. Accessed March 05, 2021. http://hdl.handle.net/10217/195411.

MLA Handbook (7^th Edition):

Eddy, Thomas D. “Improved stick number upper bounds.” 2019. Web. 05 Mar 2021.

Vancouver:

Eddy TD. Improved stick number upper bounds. [Internet] [Masters thesis]. Colorado State University; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10217/195411.

Council of Science Editors:

Eddy TD. Improved stick number upper bounds. [Masters Thesis]. Colorado State University; 2019. Available from: http://hdl.handle.net/10217/195411

University of Oxford

30. Roeser, Markus Karl. The ASD equations in split signature and hypersymplectic geometry.

Degree: PhD, 2012, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581122

► This thesis is mainly concerned with the study of hypersymplectic structures in gauge theory. These structures arise via applications of the hypersymplectic quotient construction to… (more)

Subjects/Keywords: 530.1435; Differential geometry; Hypersymplectic Geometry; Gauge Theory; Symplectic Geometry; Moduli Space; Moment Map; special Holonomy

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Roeser, M. K. (2012). The ASD equations in split signature and hypersymplectic geometry. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581122

Chicago Manual of Style (16^th Edition):

Roeser, Markus Karl. “The ASD equations in split signature and hypersymplectic geometry.” 2012. Doctoral Dissertation, University of Oxford. Accessed March 05, 2021. http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581122.

MLA Handbook (7^th Edition):

Roeser, Markus Karl. “The ASD equations in split signature and hypersymplectic geometry.” 2012. Web. 05 Mar 2021.

Vancouver:

Roeser MK. The ASD equations in split signature and hypersymplectic geometry. [Internet] [Doctoral dissertation]. University of Oxford; 2012. [cited 2021 Mar 05]. Available from: http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581122.

Council of Science Editors:

Roeser MK. The ASD equations in split signature and hypersymplectic geometry. [Doctoral Dissertation]. University of Oxford; 2012. Available from: http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581122

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