The stringy Chow ring of the moduli stack of genus-two curves and its Deligne-Mumford compactification

Let $M2$ denote the moduli stack of smooth connected genus-two curves and let $M2$ denote its Deligne-Mumford compactification. In this dissertation I consider the problem of computing the Stringy Chow rings of these stacks. The Stringy Chow ring of a stack is the Chow group of its inertia stack with a product derived from the intersection theory of a related moduli stack.; This dissertation contains the calculations of the Stringy Chow rings of $M2,M2,$ and several related stacks. In the course of this investigation, the various inertia stacks are studied directly, and I provide explicit descriptions of the connected components of the coarse moduli spaces of these stacks, including calculating many of the relevant invariants.