Kisin, MarkLam, Yeuk Hay Joshua2021-07-1320212021-05-142021-05Lam, Yeuk Hay Joshua. 2021. The Attractor Conjecture. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28499096https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368407This thesis studies the Attractor Conjecture due to Moore, which aims to produce arithmetic Calabi-Yau varieties using the attractor mechanism studied in string theory. The first part of this thesis gives counterexamples to the Attractor Conjecture in all odd dimensions except for a few small exceptions, assuming a standard conjecture in unlikely intersection theory. Our counterexamples come from a family of Calabi-Yau varieties first studied by Dolgachev, and we use crucially a transcendence result of Shiga-Wolfart. For this family of Dolgachev varieties, the conjecture holds if and only if the moduli space is a Shimura variety. The second part of this thesis proves the Attractor Conjecture in many cases of Calabi-Yau variations of Hodge structures (CYVHS) on Shimura varieties. More precisely, we study the canonical CYVHS on Shimura varieties constructed by Gross, and prove that attractor points are CM points.application/pdfenMathematicsThesis or Dissertation2021-07-130000-0001-5475-2396