9401422 Koch Professor Koch is investigating spin models relevant to the theory of critical phenomena, neural network models related to disordered systems in statistical mechanics and variational problems for non-periodic orbits and configurations. the techniques and results from previous work on hierarchical models are applied and extended to a larger class of ferromagnetic models. The investigation of neural networks focuses on large general purpose associative memories of the type of Hopfield's model with thermal noise. The third project deals with variational problems for nontrivial orbits and ground states of dynamical systems and statistical mechanics models, respectively. 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 problems in statistical mechanics and quantum field theory. ***
