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dc.contributor.advisorAthreya, Jayadev
dc.contributor.authorSoutherland, Joshua
dc.date.accessioned2019-08-14T22:36:16Z
dc.date.available2019-08-14T22:36:16Z
dc.date.submitted2019
dc.identifier.otherSoutherland_washington_0250O_19858.pdf
dc.identifier.urihttp://hdl.handle.net/1773/44368
dc.descriptionThesis (Master's)--University of Washington, 2019
dc.description.abstractThis thesis is a historical survey of the Laplacian as an operator on $L^2$-functions specifically geared towards building the understanding necessary to define a Laplacian on a translation surface. The author explores the role the Laplacian has played historically in analysis and geometry, with a particular interest in the connections between the Laplacian and the geodesics. The primary thread the author follows develops a representation-theoretic perspective of the Laplacian, which proves advantageous when working on symmetric spaces. The other appeals to a functional-analytic perspective in more abstract settings. In the final section, the author proposes a starting point for defining a Laplacian on a translation surface.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.rightsCC BY
dc.subjectGeometric Analysis
dc.subjectGraph Theory
dc.subjectLaplacian
dc.subjectRepresentation Theory
dc.subjectSpectral Theory
dc.subjectTranslation Surfaces
dc.subjectMathematics
dc.subject.otherMathematics
dc.titleThe Laplacian: An Exploration and Historical Survey Tailored for Translation Surfaces
dc.typeThesis
dc.embargo.termsOpen Access


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