Mathematical Sciences: Statistical Mechanics and Quantum Field Theory

科赫教授将继续研究与临界现象理论相关的模型，以及统计力学中与无序系统相关的神经网络模型。这包括重整化群分析新技术的发展，这将他的工作与正在使用类似方法的构造量子场论联系起来。科赫教授的工作是在广为人知的数学物理领域，寻求对物理模型的深入数学理解。他的一个项目涉及对重整化群的研究，试图同时理解所有长度尺度上的相互作用。这是当今统计力学和量子场论中最重要、最鲜为人知的问题之一。

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.