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dc.contributor.advisorYau, Shing-Tung
dc.contributor.authorFan, Yu-Wei
dc.date.accessioned2019-12-12T08:05:01Z
dc.date.created2019-05
dc.date.issued2019-05-03
dc.date.submitted2019
dc.identifier.citationFan, Yu-Wei. 2019. Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:42029475*
dc.description.abstractThe present thesis studies various aspects of Calabi-Yau manifolds, including mirror symmetry, systolic geometry, and dynamical systems. We construct the mirror operation of Atiyah flop in symplectic geometry. We construct the mirror metric of the Weil-Petersson metric on the complex moduli space of Calabi-Yau manifolds, in terms of derived categories and Bridgeland stability conditions. We propose a new generalization of Loewner’s torus systolic inequality from the perspective of Calabi-Yau geometry, and prove a generalized systolic inequality for generic K3 surfaces. We study the dynamical systems formed by autoequivalences on the derived categories of Calabi-Yau manifolds, and find the first counterexamples of Kikuta-Takahashi’s conjecture on categorical entropy.
dc.description.sponsorshipMathematics
dc.format.mimetypeapplication/pdf
dc.language.isoen
dash.licenseLAA
dc.subjectCalabi-Yau manifolds
dc.subjectmirror symmetry
dc.subjectautoequivalences
dc.subjectBridgeland stability conditions
dc.titleMirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions
dc.typeThesis or Dissertation
dash.depositing.authorFan, Yu-Wei
dc.date.available2019-12-12T08:05:01Z
thesis.degree.date2019
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.levelDoctoral
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
thesis.degree.nameDoctor of Philosophy
dc.contributor.committeeMemberAuroux, Denis
dc.contributor.committeeMemberSeidel, Paul
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.departmentMathematics
dash.identifier.vireo
dc.identifier.orcid0000-0002-6763-8872
dash.author.emailyuweifanx@gmail.com


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