Yau, Shing-TungFan, Yu-Wei2019-12-122019-052019-05-032019Fan, Yu-Wei. 2019. Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029475The 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.application/pdfenCalabi-Yau manifoldsmirror symmetryautoequivalencesBridgeland stability conditionsThesis or Dissertation2019-12-120000-0002-6763-8872