Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions
CitationFan, Yu-Wei. 2019. Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
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.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:42029475
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