{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/277369"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/277369","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"Surface multi-space","abstract":"Multi-space for curves was defined by Peter Olver to provide geometric foundationsfor symmetry methods in the numerical analysis of ordinary differential equations. Here we define multi-space for surfaces, thereby extending the framework to partial differential equations in two independent variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. We begin the study of prolongations of group actions, their invariants, and the process of extending a differential equation to multi-space, whereby the resulting equation encompasses both the original differential equation and a family of difference equations approximating it.","abstract_html":"Multi-space for curves was defined by Peter Olver to provide geometric foundationsfor symmetry methods in the numerical analysis of ordinary differential equations. Here we define multi-space for surfaces, thereby extending the framework to partial differential equations in two independent variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. 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Major: Mathematics. Advisor: Peter Olver. 1 computer file (PDF); viii, 164 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["Multi-space for curves was defined by Peter Olver to provide geometric foundationsfor symmetry methods in the numerical analysis of ordinary differential equations. Here we define multi-space for surfaces, thereby extending the framework to partial differential equations in two independent variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. We begin the study of prolongations of group actions, their invariants, and the process of extending a differential equation to multi-space, whereby the resulting equation encompasses both the original differential equation and a family of difference equations approximating it."]},{"key":"dc:title","label":"Title","values":["Surface multi-space"]}]}],"canonical_facts":{"dc:creator":["Karlsson, Jonas"],"dc:date.accessioned":["2025-12-12T11:28:44Z"],"dc:date.available":["2025-12-12T11:28:44Z"],"dc:date.issued":["2025"],"dc:description":["University of Minnesota Ph.D. dissertation. 2025. Major: Mathematics. Advisor: Peter Olver. 1 computer file (PDF); viii, 164 pages."],"dc:description.abstract":["Multi-space for curves was defined by Peter Olver to provide geometric foundationsfor symmetry methods in the numerical analysis of ordinary differential equations. Here we define multi-space for surfaces, thereby extending the framework to partial differential equations in two independent variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. We begin the study of prolongations of group actions, their invariants, and the process of extending a differential equation to multi-space, whereby the resulting equation encompasses both the original differential equation and a family of difference equations approximating it."],"dc:identifier.uri":["https://hdl.handle.net/11299/277369"],"dc:language.iso":["en"],"dc:subject":["Geometry","Numerical analysis","Symmetry"],"dc:title":["Surface multi-space"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:20:09Z"}