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Title: The arithmetic geometry of mirror symmetry and the conifold transition
Author: Yang, Wenzhe
ISNI:       0000 0004 7430 7769
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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The central theme of this thesis is the application of mirror symmetry to the study of the arithmetic geometry of Calabi-Yau threefolds. It formulates a conjecture about the properties of the limit mixed Hodge structure at the large complex structure limit of an arbitrary mirror threefold, which is supported by a two-parameter example of a self-mirror Calabi-Yau threefold. It further studies the connections between this conjecture with Voevodsky's mixed motives. This thesis also studies the connections between the conifold transition and Beilinson's conjecture on the values of the L-functions at integral points. It carefully studies the arithmetic geometry of the conifold in the mirror family of the quintic Calabi-Yau threefold and its L-function, which is shown to provide a very interesting example to Beilinson's conjecture.
Supervisor: Candelas, Philip Sponsor: Oxford-Palmer Scholarship
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mirror symmetry ; String models ; Number theory ; Algrebraic geometry ; Calabi-Yau threefold ; limit mixed Hodge structure ; conifold ; L-function ; large complex structure limit ; mixed motives