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O-minimality, nonclassical modular functions and diophantine problems

Abstract:

There now exists an abundant collection of conjectures and results, of various complexities, regarding the diophantine properties of Shimura varieties. Two central such statements are the Andre-Oort and Zilber-Pink Conjectures, the first of which is known in many cases, while the second is known in very few cases indeed.

The motivating result for much of this document is the modular case of the Andre-Oort Conjecture, which is a theorem of Pila. It is most commonly viewed as a st...

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Department:
University of Oxford (Lincoln/Mathematical Institute)
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Author, Copyright Holder

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Department:
University of Oxford (Wolfson/Mathematical Institute)
Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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