{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124365"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124365","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Duistermaat-Heckman measures for Hamiltonian groupoid actions","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_has_math":false,"creators":["Zwaan, Luka Marinus Simon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Loja Fernandes, Rui A","Lerman, Eugene M","Junge, Marius","Berwick Evans, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-22T22:25:00Z","subjects":["Poisson Manifolds","Hamiltonian Actions","Symplectic Groupoids","Integral Affine Structures"],"languages":["en","eng"],"rights":["Copyright 2024 Luka Marinus Simon Zwaan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124365","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Loja Fernandes, Rui A","Lerman, Eugene M","Junge, Marius","Berwick Evans, Daniel"]},{"key":"dc:creator","label":"Author","values":["Zwaan, Luka Marinus Simon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-05","2024-04-23"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Poisson Manifolds","Hamiltonian Actions","Symplectic Groupoids","Integral Affine Structures"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Luka Marinus Simon Zwaan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124365"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Luka Zwaan, accepted the attached license on 2024-04-22 at 15:20.","The student, Luka Zwaan, submitted this Dissertation for approval on 2024-04-22 at 15:30.","This Dissertation was approved for publication on 2024-04-23 at 16:24.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20545 on 2024-09-16 at 00:35:47","This thesis treats two problems related to Poisson manifolds of compact types: the existence of Poisson manifolds of strong compact type, and the generalisation of classical Duistermaat-Heckman results to the setting of Hamiltonian actions of symplectic groupoids. In Chapter 4 we prove that all strongly affine circles and 2-tori appear as the leaf space of a regular Poisson manifold of strong compact type. These Poisson manifolds are all fibrations over their leaf space with symplectic leaves diffeomorphic to the smooth manifold underlying a K3 surface. In Chapter 5 we show that for a Hamiltonian action of a regular, source proper symplectic groupoid with sufficiently nice properties there is an analogue of the Duistermaat-Heckman measure which is a polynomial measure with respect to the natural integral affine structure."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Duistermaat-Heckman measures for Hamiltonian groupoid actions"]}]}],"canonical_facts":{"dc:contributor":["Loja Fernandes, Rui A","Lerman, Eugene M","Junge, Marius","Berwick Evans, Daniel"],"dc:creator":["Zwaan, Luka Marinus Simon"],"dc:date":["2024-05","2024-04-23"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Luka Zwaan, accepted the attached license on 2024-04-22 at 15:20.","The student, Luka Zwaan, submitted this Dissertation for approval on 2024-04-22 at 15:30.","This Dissertation was approved for publication on 2024-04-23 at 16:24.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20545 on 2024-09-16 at 00:35:47","This thesis treats two problems related to Poisson manifolds of compact types: the existence of Poisson manifolds of strong compact type, and the generalisation of classical Duistermaat-Heckman results to the setting of Hamiltonian actions of symplectic groupoids. In Chapter 4 we prove that all strongly affine circles and 2-tori appear as the leaf space of a regular Poisson manifold of strong compact type. These Poisson manifolds are all fibrations over their leaf space with symplectic leaves diffeomorphic to the smooth manifold underlying a K3 surface. In Chapter 5 we show that for a Hamiltonian action of a regular, source proper symplectic groupoid with sufficiently nice properties there is an analogue of the Duistermaat-Heckman measure which is a polynomial measure with respect to the natural integral affine structure."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124365"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Luka Marinus Simon Zwaan"],"dc:subject":["Poisson Manifolds","Hamiltonian Actions","Symplectic Groupoids","Integral Affine Structures"],"dc:title":["Duistermaat-Heckman measures for Hamiltonian groupoid actions"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:00Z"}