Professor John Imbrie is an outstanding, young mathematical physicist who has made significant contributions to our understanding of constructive quantum field theory and of disordered systems. His proof of the existence of a long range order for the three dimensional random-field Ising model was a major advancement for the field. He now proposes to investigate the behavior of directed polymers in a random environment and to develop rigorous renormalization group methods for gauge theories. He also plans to study interacting walks, such as the self-avoiding walk in four dimensions. Two of the most interesting problems in condensed matter physics and high energy physics have to do with disordered systems and quantum field theory, respectively. Professor Imbrie's research on these problems has been excellent, advancing our knowledge significantly. He proposes to continue and to expand his research in these areas. These are difficult problems, but if Professor Imbrie can solve them, their impact on the scientific community will be important. For example, applied physics and chemistry are concerned about his work on the behavior of directed polymers. Funding for this exciting and fundamental research is strongly recommended.
