{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90563"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90563","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Finite order automorphisms of Higgs bundles: theory and application","abstract":"DSpace SAF Submission Ingestion Package generated from Vireo submission #9304 on 2016-07-07 at 13:31:11","abstract_html":"DSpace SAF Submission Ingestion Package generated from Vireo submission #9304 on 2016-07-07 at 13:31:11","abstract_has_math":false,"creators":["Collier, Brian Patrick"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bradlow, Steve","Nevins, Tom","Bergvelt, Maarten","Albin, Pierre"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T19:54:09Z","date_published":"2016-07-07T19:54:09Z","updated_at":"2026-07-22T22:26:32Z","subjects":["Higgs bundles","Character varieties"],"languages":["en"],"rights":["Copyright 2016 Brian Collier"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90563","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bradlow, Steve","Nevins, Tom","Bergvelt, Maarten","Albin, Pierre"]},{"key":"dc:creator","label":"Author","values":["Collier, Brian Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T19:54:09Z","2016-04-21","2016-05"]},{"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":["Higgs bundles","Character varieties"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Brian Collier"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90563"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["DSpace SAF Submission Ingestion Package generated from Vireo submission #9304 on 2016-07-07 at 13:31:11","Made available in DSpace on 2016-07-07T19:54:09Z (GMT). No. of bitstreams: 3 COLLIER-DISSERTATION-2016.pdf: 943323 bytes, checksum: f7c8542394ec846e354178adc07c5c0a (MD5) LICENSE.txt: 4210 bytes, checksum: 1925f0e6e0a75561683a7797eaf20032 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 5da0980478834a3b041214400b8ae7c0 (MD5) Previous issue date: 2016-04-21","We study G-Higgs bundles over a Riemann surface which are fixed points of a roots of unity action. When G is complex we classify such fixed points and study certain lifting properties of the corresponding harmonic metric. This remainder of the thesis is devoted to applications. In particular, parameterize the space of maximal SO(2,3) surface group representations as fiber bundles over Teichmuller space. We also show that there are many new connected components of the SO(n,n+1) character variety.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms","The student, Brian Collier, accepted the attached license on 2016-04-18 at 14:26.","The student, Brian Collier, submitted this Dissertation for approval on 2016-04-20 at 11:51.","This Dissertation was approved for publication on 2016-04-21 at 08:48."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Finite order automorphisms of Higgs bundles: theory and application"]}]}],"canonical_facts":{"dc:contributor":["Bradlow, Steve","Nevins, Tom","Bergvelt, Maarten","Albin, Pierre"],"dc:creator":["Collier, Brian Patrick"],"dc:date":["2016-07-07T19:54:09Z","2016-04-21","2016-05"],"dc:description":["DSpace SAF Submission Ingestion Package generated from Vireo submission #9304 on 2016-07-07 at 13:31:11","Made available in DSpace on 2016-07-07T19:54:09Z (GMT). No. of bitstreams: 3 COLLIER-DISSERTATION-2016.pdf: 943323 bytes, checksum: f7c8542394ec846e354178adc07c5c0a (MD5) LICENSE.txt: 4210 bytes, checksum: 1925f0e6e0a75561683a7797eaf20032 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 5da0980478834a3b041214400b8ae7c0 (MD5) Previous issue date: 2016-04-21","We study G-Higgs bundles over a Riemann surface which are fixed points of a roots of unity action. When G is complex we classify such fixed points and study certain lifting properties of the corresponding harmonic metric. This remainder of the thesis is devoted to applications. In particular, parameterize the space of maximal SO(2,3) surface group representations as fiber bundles over Teichmuller space. We also show that there are many new connected components of the SO(n,n+1) character variety.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms","The student, Brian Collier, accepted the attached license on 2016-04-18 at 14:26.","The student, Brian Collier, submitted this Dissertation for approval on 2016-04-20 at 11:51.","This Dissertation was approved for publication on 2016-04-21 at 08:48."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/90563"],"dc:language":["en"],"dc:rights":["Copyright 2016 Brian Collier"],"dc:subject":["Higgs bundles","Character varieties"],"dc:title":["Finite order automorphisms of Higgs bundles: theory and application"],"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":"2026-07-22T22:26:32Z"}