The noncommutative geometry of the Landau Hamiltonian

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dc.catalogadorgjm
dc.contributor.advisorDe Nittis, Giuseppe
dc.contributor.authorSandoval, Maximiliano
dc.contributor.otherPontificia Universidad Católica de Chile. Facultad de Matemáticas
dc.date.accessioned2024-06-17T14:27:12Z
dc.date.available2024-06-17T14:27:12Z
dc.date.issued2024
dc.date.updated2024-06-16T22:45:08Z
dc.descriptionTesis (Doctor in Mathematics)--Pontificia Universidad Católica de Chile, 2024.
dc.description.abstractThis dissertation will present three works in the areas of noncommutative geometry, the study of the Landau Hamiltonian, and the study of rational noncommutative tori making use of complex geometry and theta functions. The first two works focus primary on extending Bellissard’s work on the noncommutative geometry of the Hall Effect to the case where the medium is continuous case making use of a novel Dirac Operator, closely related to the isotropic quantum harmonic oscillator. We study the resulting spectral triple and its properties as a noncommutative space. Notably we provide proofs for the first and second Connes formulas for this spectral triple. The third work deals with the study of a pair of dual representations of rational noncommutative tori with rational parameters θ and θ −1, how we can naturally construct a vector bundles on a complex tori from to them, and hint how this duality is a manifestation of the Fourier-Mukai-Nahm transform.
dc.fechaingreso.objetodigital2024-06-17
dc.format.extentix, 174 páginas
dc.fuente.origenAutoarchivo
dc.identifier.doi10.7764/tesisUC/MAT/86796
dc.identifier.urihttps://doi.org/10.7764/tesisUC/MAT/86796
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/86796
dc.information.autorucFacultad de Matemáticas; De Nittis, Giuseppe; 0000-0001-6066-8625; 1019873
dc.information.autorucFacultad de Matemáticas; Sandoval, Maximiliano; 0000-0002-9129-9153; 1071086
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.rights.licenseAtribución-CompartirIgual 4.0 Internacional (CC BY-SA 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/deed.es
dc.subjectHamiltoniano de Landau
dc.subjectTriples espectrales
dc.subjectGeometría no conmutativa
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.subject.ods09 Industry, innovation and infrastructure
dc.subject.odspa09 Industria, innovación e infraestructura
dc.titleThe noncommutative geometry of the Landau Hamiltonian
dc.typetesis doctoral
sipa.codpersvinculados1019873
sipa.codpersvinculados1071086
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