Includes bibliographical references (pages 214-240) and indexes.
Contents:
Point-counting -- Multiplicative Manin-Mumford -- Powers of the modular curve as Shimura varieties -- Modular André-Oort -- Point-counting and the André-Oort conjecture -- Model theory and definable sets -- O-minimal structures -- Parameterization and point-counting -- Better bounds -- Point-counting and Galois orbit bounds -- Complex analysis in O-minimal structures -- Schanuel's conjecture and Ax-Schanuel -- A formal setting -- Modular Ax-Schanuel -- Ax-Schanuel for Shimura varieties -- Quasi-periods of elliptic curves -- Sources -- Formulations -- Some results -- Curves in a power of the modular curve -- Conditional modular Zilber-Pink -- O-minimal uniformity -- Uniform Zilber-Pink.
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