{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/145087"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/145087","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Genera via Deformation Theory and Supersymmetric Mechanics","abstract":"We study naturally occurring genera (i.e. cobordism invariants) from the deformation theory in- spired by supersymmetric quantum mechanics. First, we construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish in the super-symplectic setting. In the second part of this thesis, we prove a super-version of Nest-Tsygan’s algebraic index theorem, generalizing work of Engeli. This work is inspired by the appearance of the same genera in three related stories: index theory, trace methods in deformation theory, and partition functions in quantum field theory. Using the trace methodology, we compute the genus appearing in the story for supersymmetric quantum mechanics. This involves investigating supertraces on Weyl-Clifford algebras and deformations of symplectic supermanifolds.","abstract_html":"We study naturally occurring genera (i.e. cobordism invariants) from the deformation theory in- spired by supersymmetric quantum mechanics. First, we construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish in the super-symplectic setting. In the second part of this thesis, we prove a super-version of Nest-Tsygan’s algebraic index theorem, generalizing work of Engeli. This work is inspired by the appearance of the same genera in three related stories: index theory, trace methods in deformation theory, and partition functions in quantum field theory. Using the trace methodology, we compute the genus appearing in the story for supersymmetric quantum mechanics. This involves investigating supertraces on Weyl-Clifford algebras and deformations of symplectic supermanifolds.","abstract_has_math":false,"creators":["Wilson, Araminta Amabel"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Hopkins, Michael J."],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:21:37Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/145087","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hopkins, Michael J."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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First, we construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish in the super-symplectic setting. In the second part of this thesis, we prove a super-version of Nest-Tsygan’s algebraic index theorem, generalizing work of Engeli. This work is inspired by the appearance of the same genera in three related stories: index theory, trace methods in deformation theory, and partition functions in quantum field theory. Using the trace methodology, we compute the genus appearing in the story for supersymmetric quantum mechanics. This involves investigating supertraces on Weyl-Clifford algebras and deformations of symplectic supermanifolds."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Genera via Deformation Theory and Supersymmetric Mechanics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hopkins, Michael J."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics"],"dc:creator":["Wilson, Araminta Amabel"],"dc:date.accessioned":["2022-08-29T16:31:57Z"],"dc:date.available":["2022-08-29T16:31:57Z"],"dc:date.issued":["2022-05"],"dc:description.abstract":["We study naturally occurring genera (i.e. cobordism invariants) from the deformation theory in- spired by supersymmetric quantum mechanics. First, we construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish in the super-symplectic setting. In the second part of this thesis, we prove a super-version of Nest-Tsygan’s algebraic index theorem, generalizing work of Engeli. This work is inspired by the appearance of the same genera in three related stories: index theory, trace methods in deformation theory, and partition functions in quantum field theory. Using the trace methodology, we compute the genus appearing in the story for supersymmetric quantum mechanics. This involves investigating supertraces on Weyl-Clifford algebras and deformations of symplectic supermanifolds."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/145087"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Genera via Deformation Theory and Supersymmetric Mechanics"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:21:37Z"}