Mathematical Sciences: RUI: Factorization of Modular Invariants and Heights of Heegner Points

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This research will focus on two problems in algebraic geometry. The first is to produce a factorization of a certain invariant associated to a particular algebraic curve called the classical modular curve of level N where N is a positive integer. The second problem is the computation of the heights special points, called Heegner points, on Drinfeld modular curves. This investigation will entail the study of the endomorphism rings of rank 2 Drinfeld modules having supersingular reduction and orders in definite quaternion algebras. This project is in the general area of algebraic geometry. Algebraic geometry concerns the study of the curves and surfaces that arise naturally as the sets of solutions of one or more algebraic equations.