Toric Degenerations of Calabi-Yau Manifolds in Grassmannians

We describe methods for constructing toric degenerations of Calabi-Yau manifolds in Grassmannians. Toric degenerations were introduced by Gross and Siebert in their work on mirror symmetry, and consist of a one-parameter family of algebraic varieties with a certain type of singular fiber. Gross showed that toric degenerations give, in a certain sense, a complete description of Calabi-Yau manifolds that arise from the Batyrev-Borisov construction. This thesis focuses on Calabi-Yau complete intersections in Grassmannians, which in general cannot be obtained from the Batyrev-Borisov construction. We completely work out the details of the simplest example, that of a quartic hypersurface in G(2, 4), and discuss how a similar strategy might be used in higher-dimensional cases.