The ambitious goal of modern subatomic theory is the unification of all of the fundamental forces. At present, the standard model is believed to explain the basic principles of all non-gravitational interactions of subatomic physics. However, the unification of gravity with the subatomic forces has proven to be a most difficult problem. Although there are different approaches to quantizing gravity and carrying out a unification of all fundamental forces, string theory is thus far the most successful. However, many key issues in this approach are not yet completely understood. Although string theory provides a renormalizable field theory containing a graviton, it is still unclear how Einstein gravity and 4-dimensional spacetime emerge from this theory. My research interests are concentrated on understanding these issues,in particular the role that topology and global geometry play in classical and quantum field theory and string theory. In particular, I am looking at the global structure of string theory and gravity and using global techniques to obtain a deeper understanding of key connections between these seemingly disparate theories. Recently, intriguing clues about these connections have been found: the derivation of black hole entropy from string theory, the AdS/CFT correspondence which may provide a deep connection between string theory and causality in Einstein gravity, and the possiblility of induced negative energy densities from Calabi-Yau compactifications providing counterexamples to cosmic censorship. I intend to investigate certain facets of these three important topics using topological and global techniques to obtain a fuller understanding the connections of string theory to gravity. I am also using techniques from string theory and gravity to solve interesting problems in mathematics, namely the structure of the diffeomorphism group on 3-manifolds.