2026-09-19T09:55:18Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/1159602026-05-15T19:50:09Zcom_1813_35col_1813_47
Magill, Nicole
Riley, Tara
Manning, Jason
Knutson, Allen
2024-11-05T19:46:41Z
2024-11-05T19:46:41Z
2024-05
ProQuest Submission ID: 14254
ProQuest Publication ID: 31241996
https://hdl.handle.net/1813/115960
https://doi.org/10.7298/5ngq-yw35
16575581
148 pages
This thesis gives a classification of infinite staircases for the ellipsoid embedding functions of Hirzebruch surfaces. The ellipsoid embedding function is a generalization of symplectic ball packing problems. For a symplectic manifold, the function gives the smallest amount of which the symplectic form must be scaled in order for a standard ellipsoid of a given eccentricity to embed symplectically into the manifold. Generally, there are only finitely many obstructions other than the volume obstruction relevant to compute the function. If there are infinitely many obstructions, the function is said to have an infinite staircase. This classification problem was studied in a series of five papers written by: Bertozzi-Holm-Maw-McDuff-Mwakyoma-Pires-Weiler, Magill-McDuff, Magill-McDuff-Weiler, Magill, and Magill-Pires-Weiler. The thesis contains two of these papers and includes a summary of the results of the other papers.
en
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
Infinite staircases for Hirzebruch surfaces
dissertation or thesis
https://newcatalog.library.cornell.edu/catalog/16575581
application/pdf
Mathematics
Cornell University
Doctor of Philosophy
Ph. D., Mathematics
https://hdl.handle.net/1813/59810.2
Publication
Cornell Theses and Dissertations
Magill, Nicole
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
open.access
open.access
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<Abstract>This thesis gives a classification of infinite staircases for the ellipsoid embedding functions of Hirzebruch surfaces. The ellipsoid embedding function is a generalization of symplectic ball packing problems. For a symplectic manifold, the function gives the smallest amount of which the symplectic form must be scaled in order for a standard ellipsoid of a given eccentricity to embed symplectically into the manifold. Generally, there are only finitely many obstructions other than the volume obstruction relevant to compute the function. If there are infinitely many obstructions, the function is said to have an infinite staircase. This classification problem was studied in a series of five papers written by: Bertozzi-Holm-Maw-McDuff-Mwakyoma-Pires-Weiler, Magill-McDuff, Magill-McDuff-Weiler, Magill, and Magill-Pires-Weiler. The thesis contains two of these papers and includes a summary of the results of the other papers.</Abstract>
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