Geometry of Strings and Gravity

Harvard University, Cambridge MA

Investigators

Abstract

Problems of fundamental physics in the context of string theory and gravity can often be rephrased purely as problems in geometry, the space of vacua of string theory and in particular the spectrum of supersymmetric (BPS) objects on them. On certain "walls" in the moduli space of vacua, a BPS object can decay to less massive BPS objects. Such a wallcrossing phenomenon has an extremely rich and mysterious mathematical structure. It is proposed to study wall-crossings from various points of views including vacua with high number of supersymmetries, applying tools of mirror symmetry and string dualities. Understanding the spectrum of BPS objects is important for calculating black hole entropy and topological string theory. The PI proposes to uncover new geometrical invariants which are necessary for physically characterizing these string vacua, and explore the implications of a recently defined quasi-local mass which satisfies all known consistency conditions. The projects address exciting questions that have important implications for theoretical physics, and for differential and algebraic geometry. Central to the proposal is the training of postdoctoral fellows and graduate students to conduct cutting edge cross-disciplinary research and to be effective in interacting with both the physics and mathematics communities.