The Attractor Conjecture
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Lam, Yeuk Hay Joshua
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CitationLam, Yeuk Hay Joshua. 2021. The Attractor Conjecture. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.
AbstractThis 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.
Citable link to this pagehttps://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368407
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