This award funds the research activities of Professor Jeffrey Harvey at the University of Chicago.
With the discovery of the Higgs boson, the Standard Model of particle physics is now complete, but there are still many important outstanding questions involving the fundamental structure of matter and energy and their interactions. These include understanding what sorts of mathematical structures are needed to combine gravity and quantum mechanics, as well as to understand the origin of dark matter and dark energy. String theory provides one possible framework in which to address these questions. Part of this project is devoted to the study of new mathematical structures which have been discovered in string theory and which are closely connected to the area of mathematics that studies the properties of whole numbers. These new mathematical structures are also relevant to the study of topics such as the structure of new types of materials called topological insulators and perhaps even to the study of physical systems which may be used to construct quantum computers. This project will also have broader impacts beyond the generation of new knowledge. It will involve postdocs, graduate students, and at times undergraduate students, and will provide critical training for the next generation of physicists as they start research. This pool of technical knowledge provides the foundation for much of the technology developed by the United States, and enhancing this pool of knowledge is therefore in the national interest. The PI will also lecture at international schools and workshops and in public-outreach events in the Chicago area.
More technically, the PI will extend his past work on the role of Hecke operators in two-dimensional conformal field theory and investigate possible applications both to mathematical physics and to various systems in condensed-matter physics where conformal field theory plays a central role. He also plans to work on new developments concerning connections between modular forms and the representation theory of finite groups, and to explore the physics of non-compact conformal field theories and their connections to mock modular forms and to black-hole entropy in string theory.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
