### MATHEMATICAL PHYSICS

Many contemporary problems arising in physics are often too difficult to solve exactly by analytical means. Computer assisted studies are very useful substitutes, but they have their limitations. Applying modern mathematical methods to generate estimates and/or controlled bounds on relevant quantities, or even simply to generate new insights into old problems by the study of specialized models can sometimes provide an alternative approach.

Current efforts in mathematical physics are addressed to questions in quantum mechanics, functional integration, quantum field theory, quantum gravity, various topics in condensed matter physics, etc. The range of applications is very broad.

One specific recent example involves the use of coherent state methods to study the quantization of the gravitational field. As part of this study it is found that noncanonical methods are often required in order to respect certain aspects of the basic physics of the problem. This emphasis as well as the methods involved sets this method apart from other current approaches to study quantum gravity.

In another example, methods of mathematical physics are developed and used to explore universal features in exactly solvable random matrix models that go beyond the well-known Wigner-Dyson Gaussian ensembles. Such models provide useful insights into real physical systems where perturbative approaches fail due to a variety of reasons.