This research will study the moduli stacks of abelian schemes over the integers with level structures. It will also investigate the intersections of the different components of the moduli space of polarized abelian varieties over a field of characteristic p > 0. This research studies the number theoretic-algebraic geometric object called an abelian variety. This is the geometric interpretation of the object one studies in number theory in attempting to solve diophantine equations, i.e. solutions of polynomial equations in integers. Dr. Norman is a very deep worker in this area who has already embarked on this project with very promising results so far. This work should lead to very exciting further results.
