{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/125537"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/125537","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Shifted symplectic structures and derived moduli spaces","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","abstract_has_math":false,"creators":["Adhikari, Nachiketa"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Katz, Sheldon","Heller, Jeremiah","Dodd, Christopher","Janda, Felix"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-06-26","date_published":"2024-06-26","updated_at":"2026-07-22T22:25:02Z","subjects":["Algebraic Geometry","Moduli Spaces","Derived Stacks","Shifted Symplectic Structures","Quot Scheme","Hilbert Scheme","Coherent Sheaves","Calabi-yau Manifolds"],"languages":["en","eng"],"rights":["Copyright 2024 Nachiketa Adhikari"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/125537","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Katz, Sheldon","Heller, Jeremiah","Dodd, Christopher","Janda, Felix"]},{"key":"dc:creator","label":"Author","values":["Adhikari, Nachiketa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-06-26","2024-08"]},{"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":["Algebraic Geometry","Moduli Spaces","Derived Stacks","Shifted Symplectic Structures","Quot Scheme","Hilbert Scheme","Coherent Sheaves","Calabi-yau Manifolds"]}]},{"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 Nachiketa Adhikari"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/125537"]}]},{"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 2025-02-04 without embargo terms","The student, Nachiketa Adhikari, accepted the attached license on 2024-06-25 at 15:36.","The student, Nachiketa Adhikari, submitted this Dissertation for approval on 2024-06-25 at 15:45.","This Dissertation was approved for publication on 2024-06-26 at 16:22.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20872 on 2025-02-04 at 21:03:55","Derived algebraic geometry is a vast generalization of algebraic geometry that involves higher categories in a fundamental way. Constructions of derived moduli spaces and their intrinsic features as derived objects (for example, the cotangent complex, higher morphism spaces) have proved instrumental in understanding the behavior of many ordinary moduli spaces. This in turn has facilitated advancements in enumerative geometry (among other fields), especially that of Calabi-Yau threefolds and fourfolds. This thesis, after providing a brief introduction to the derived algebraic framework developed by Toën-Vezzosi and Lurie, builds on existing work of Toën-Vaquié to prove the existence and representability of the derived quot scheme. This derived moduli space is in a natural way a generalization of the ordinary quot scheme, which, while crucial for constructing several other interesting moduli spaces, is also interesting in its own right. Shifted symplectic structures, introduced by Pantev-Toën-Vaquié-Vezzosi, are extensions of ordinary symplectic structures to the derived setting. They capture several phenomena seen at the classical level, such as symmetric obstruction theories, while also shedding light on new phenomena. This thesis (including joint work with Yun Shi described in Sections 4.3 and 4.4) builds on work of Brav-Bussi-Joyce to show that certain shifted symplectic derived spaces (including moduli spaces of coherent sheaves on fourfolds) can be locally obtained as derived critical loci."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Shifted symplectic structures and derived moduli spaces"]}]}],"canonical_facts":{"dc:contributor":["Katz, Sheldon","Heller, Jeremiah","Dodd, Christopher","Janda, Felix"],"dc:creator":["Adhikari, Nachiketa"],"dc:date":["2024-06-26","2024-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","The student, Nachiketa Adhikari, accepted the attached license on 2024-06-25 at 15:36.","The student, Nachiketa Adhikari, submitted this Dissertation for approval on 2024-06-25 at 15:45.","This Dissertation was approved for publication on 2024-06-26 at 16:22.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20872 on 2025-02-04 at 21:03:55","Derived algebraic geometry is a vast generalization of algebraic geometry that involves higher categories in a fundamental way. Constructions of derived moduli spaces and their intrinsic features as derived objects (for example, the cotangent complex, higher morphism spaces) have proved instrumental in understanding the behavior of many ordinary moduli spaces. This in turn has facilitated advancements in enumerative geometry (among other fields), especially that of Calabi-Yau threefolds and fourfolds. This thesis, after providing a brief introduction to the derived algebraic framework developed by Toën-Vezzosi and Lurie, builds on existing work of Toën-Vaquié to prove the existence and representability of the derived quot scheme. This derived moduli space is in a natural way a generalization of the ordinary quot scheme, which, while crucial for constructing several other interesting moduli spaces, is also interesting in its own right. Shifted symplectic structures, introduced by Pantev-Toën-Vaquié-Vezzosi, are extensions of ordinary symplectic structures to the derived setting. They capture several phenomena seen at the classical level, such as symmetric obstruction theories, while also shedding light on new phenomena. This thesis (including joint work with Yun Shi described in Sections 4.3 and 4.4) builds on work of Brav-Bussi-Joyce to show that certain shifted symplectic derived spaces (including moduli spaces of coherent sheaves on fourfolds) can be locally obtained as derived critical loci."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/125537"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Nachiketa Adhikari"],"dc:subject":["Algebraic Geometry","Moduli Spaces","Derived Stacks","Shifted Symplectic Structures","Quot Scheme","Hilbert Scheme","Coherent Sheaves","Calabi-yau Manifolds"],"dc:title":["Shifted symplectic structures and derived moduli spaces"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}