Professor Koch will continue his investigations of models relevant to the theory of critical phenomena, and of neural network models related to disordered systems in statistical mechanics. This includes the development of new techniques in renormalization group analysis, which connects his work to constructive quantum field theory, where similar methods are being used. Professor Koch's work is in the area broadly known as mathematical physics where a deep mathematical understanding of physical models is sought. One of his projects involves an investigation of the renormalization group, where an attempt is made to understand interactions at all length scales simultaneously. This is one of the most important and least understood problems in statistical mechanics and quantum field theory today.
