{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110493"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110493","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Deformations of homotopy theories via algebraic theories","abstract":"We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, we give some tools for working with K(h)-local E-infinity algebras over a Lubin-Tate spectrum of height h, and use these to produce new E-infinity complex orientations at heights h <= 2.","abstract_html":"We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, we give some tools for working with K(h)-local E-infinity algebras over a Lubin-Tate spectrum of height h, and use these to produce new E-infinity complex orientations at heights h &lt;= 2.","abstract_has_math":false,"creators":["Balderrama, William"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles","Stojanoska, Vesna","Ando, Matthew","Heller, Jeremiah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T01:11:01Z","date_published":"2021-09-17T01:11:01Z","updated_at":"2026-07-22T22:24:50Z","subjects":["Homotopy theory"],"languages":["en"],"rights":["Copyright 2021 William Balderrama"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110493","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles","Stojanoska, Vesna","Ando, Matthew","Heller, Jeremiah"]},{"key":"dc:creator","label":"Author","values":["Balderrama, William"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T01:11:01Z","2021-04-20","2021-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Homotopy theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 William Balderrama"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110493"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, we give some tools for working with K(h)-local E-infinity algebras over a Lubin-Tate spectrum of height h, and use these to produce new E-infinity complex orientations at heights h <= 2.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, William Balderrama, accepted the attached license on 2021-04-17 at 09:31.","The student, William Balderrama, submitted this Dissertation for approval on 2021-04-17 at 09:47.","This Dissertation was approved for publication on 2021-04-20 at 16:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16384 on 2021-09-16 at 16:42:24","Made available in DSpace on 2021-09-17T01:11:01Z (GMT). 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From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, we give some tools for working with K(h)-local E-infinity algebras over a Lubin-Tate spectrum of height h, and use these to produce new E-infinity complex orientations at heights h <= 2.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, William Balderrama, accepted the attached license on 2021-04-17 at 09:31.","The student, William Balderrama, submitted this Dissertation for approval on 2021-04-17 at 09:47.","This Dissertation was approved for publication on 2021-04-20 at 16:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16384 on 2021-09-16 at 16:42:24","Made available in DSpace on 2021-09-17T01:11:01Z (GMT). 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