This is a group proposal for continued support of research in general relativity and especially its interface with quantum physics. The program has several goals which will be pursued by the PIs in various collaborations. First, they hope to determine conclusively if quantum general relativity can exist as a mathematically consistent theory non-perturbatively. Second, they wish to introduce a number of new approximation methods to: i) gain physical insights into the nature of quantum geometry that is to replace the continuum and explore the effects that this replacement would have on quantum field theory; ii) study the coupling of matter fields to gravity; iii) investigate whether the requirements that the theory has a good ultra-violet behavior and a good semi-classical limit have unanticipated consequences; and, iv) explore certain aspects of the relation between string theory and quantum gravity. This program will explore the most important open problems in theoretical physics, and is likely to produce important insights and progress.
