Principal Investigator: Cumrun Vafa
This research project assembles a team at two campuses to work on string theory and related geometry. The project is led by two mathematicians and a physicist, and the award supports postdoctoral research fellows, graduate students, and the collaborations and communications of a broadly based research network. The research program supported by this award concentrates on dualities in string theory and M theory, a topic in which a broad range of geometric and physical concepts come together. The best known of these dualities is mirror symmetry, which has had dramatic consequences for algebraic and symplectic geometry, and this project intends to explore new dualities and constraints along with mirror symmetry.
String theory is a promising candidate for a unifying theory of the universe at its most fundamental levels. The basic idea is simple - elementary particles should be modeled as mathematical loops of string rather than as points - but working out the details of this theory has involved and inspired some sophisticated mathematical tools and ideas. Constraints and observations from physics, sometimes posed as a claim that two distinct geometries must generate the same physical theory, can have large numbers of consequences for geometry since quantities of physical interest are often expressed as the average value of an observable quantity over space, or as a way of counting the number of times two objects meet.