Mathematical Sciences: Statistical Mechanics and Renormalization

9401422 Koch Koch教授正在研究与临界现象理论相关的自旋模型，与统计力学中无序系统相关的神经网络模型以及非周期轨道和构型的变分问题。从以前的工作层次模型的技术和结果被应用和扩展到一个更大的类铁磁模型。神经网络的研究主要集中在热噪声的Hopfield模型类型的大型通用联想记忆。第三个项目分别处理动力系统和统计力学模型的非平凡轨道和基态的变分问题。科赫教授的工作是在被广泛称为数学物理学的领域，在这个领域中，人们寻求对物理模型进行深刻的数学理解。他的一个项目涉及对重整化群的调查，其中试图同时理解所有长度尺度上的相互作用。这是统计力学和量子场论中最重要的问题之一。＊＊＊

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. ***