{"page":"141","file":[{"relation":"source_file","date_created":"2025-11-01T18:26:14Z","file_size":72487812,"date_updated":"2025-11-01T18:26:14Z","content_type":"application/zip","file_name":"Thesis_tex.zip","access_level":"open_access","creator":"sishida","checksum":"4eef80afcb67691cbb6549c4756fa534","file_id":"20583"},{"access_level":"open_access","success":1,"creator":"sishida","checksum":"1e5a557900bf2dce01966b211b15d0fe","file_id":"20623","date_created":"2025-11-10T08:45:05Z","relation":"main_file","date_updated":"2025-11-10T08:45:05Z","file_size":8945141,"content_type":"application/pdf","file_name":"Thesis_Sadashige_Ishida_PDFA.pdf"}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"12846","status":"public"},{"relation":"part_of_dissertation","id":"12431","status":"public"},{"status":"public","id":"17361","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"20580","status":"public"}]},"year":"2025","has_accepted_license":"1","month":"10","acknowledged_ssus":[{"_id":"CampIT"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"status":"public","language":[{"iso":"eng"}],"ddc":["516"],"citation":{"short":"S. Ishida, Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space, Institute of Science and Technology Austria, 2025.","ieee":"S. Ishida, “Symplectic-prequantum structures and dynamics on the codimension-2 shape space,” Institute of Science and Technology Austria, 2025.","ama":"Ishida S. Symplectic-prequantum structures and dynamics on the codimension-2 shape space. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20551\">10.15479/AT-ISTA-20551</a>","ista":"Ishida S. 2025. Symplectic-prequantum structures and dynamics on the codimension-2 shape space. Institute of Science and Technology Austria.","chicago":"Ishida, Sadashige. “Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20551\">https://doi.org/10.15479/AT-ISTA-20551</a>.","apa":"Ishida, S. (2025). <i>Symplectic-prequantum structures and dynamics on the codimension-2 shape space</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20551\">https://doi.org/10.15479/AT-ISTA-20551</a>","mla":"Ishida, Sadashige. <i>Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20551\">10.15479/AT-ISTA-20551</a>."},"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","oa":1,"title":"Symplectic-prequantum structures and dynamics on the codimension-2 shape space","abstract":[{"lang":"eng","text":"The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D, is an infinite-dimensional manifold. This thesis explores geometric structures and dynamics on this space, with emphasis on their implications for physics, particularly hydrodynamics.\r\n\r\nOur investigation ranges from theoretical studies of infinite-dimensional symplectic and prequantum geometry to numerical computation of the time evolution of shapes. The thesis presents four main contributions.\r\n\r\nIn the first part, we introduce implicit representations of codimension-2 shapes using a class of complex-valued functions, and prove that the space of these implicit representations forms a prequantum bundle over the codimension-2 shape space. This reveals a new geometric interpretation of the canonical symplectic structure on the codimension-2 shape space.\r\n\r\nIn the second part, we use implicit representations to develop a simulation method for the dynamics of space curves. To handle chaotic systems such as vortex filaments in hydrodynamics, we exploit the infinite degrees of freedom, hidden in both the configuration and dynamics of implicit representations.\r\n\r\nIn the third part, we introduce new symplectic structures on the space of space curves, which generalize the only previously known symplectic structure on this space, allowing for new Hamiltonian dynamics of space curves.\r\n\r\nIn the fourth part, we apply a symplectic viewpoint to a differential geometric problem with practical applications. We derive a new area formula for spherical polygons via prequantization. "}],"supervisor":[{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","first_name":"Christopher J"},{"last_name":"Chern","full_name":"Chern, Albert","first_name":"Albert"}],"author":[{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","last_name":"Ishida","full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100","first_name":"Sadashige"}],"corr_author":"1","date_updated":"2025-11-14T12:28:39Z","article_processing_charge":"No","OA_place":"repository","doi":"10.15479/AT-ISTA-20551","_id":"20551","type":"dissertation","date_created":"2025-10-27T10:28:52Z","date_published":"2025-10-31T00:00:00Z","day":"31","degree_awarded":"PhD","publisher":"Institute of Science and Technology Austria","ec_funded":1,"acknowledgement":"Projects contained in this thesis were financially supported in part by the\r\nEuropean Research Council with grants 1. ERC Consolidator Grant 101045083 CoDiNA,\r\nand 2. the European Union’s Horizon 2020 research and innovation programme under grant\r\nagreement No. 638176.","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publication_identifier":{"isbn":["978-3-99078-070-1"],"issn":["2663-337X"]},"file_date_updated":"2025-11-10T08:45:05Z","project":[{"_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales","call_identifier":"H2020","grant_number":"638176"},{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"publication_status":"published"}