Mathematical Sciences: Statistical Mechanics and Quantum Field Theory

这个数学物理的项目与 严格分析了重整化群技术在一个 物理学家启发式的方式。 （基本的物理问题是 来确定大型粒子系统的宏观性质 与已知的短程相互作用。）部分工作涉及 用计算机帮助寻找证据的一种新方法 需要复杂的方案来估计的定理 是介于 重正化群技术已被证明是一种 统计力学中的有力工具，特别是在理论上， 关键现象。 同样的技术也起着主导作用， 在现代量子场论中的作用。 目前这两个领域的大部分研究都涉及到 将现有方法从相对简单扩展到更多 现实的系统。 科赫教授将继续他的 与临界理论相关的模型研究 现象。 他的第二个主要重点是分析无序的 Hopfield模型和Sherrington模型等系统， 柯克帕特里克模型，它表现出自旋玻璃行为， 一定范围的参数。

This project in mathematical physics has to do with the rigorous analysis of renormalization group techniques used in a heuristic fashion by physicists. ( The basic physical problem is to determine macroscopic properties of large systems of particles with known short range interactions. ) Some of the work involves a novel use of the computer to assist in finding proofs of theorems that require intricate schemes for estimating quantities. Renormalization group techniques have proved to be a powerful tool in statistical mechanics, especially in the theory of critical phenomena. The same techniques also play a dominant role in the modern approach to constructive quantum field theory. Much of the current research in these two areas is concerned with the extension of present methods from relatively simple to more realistic systems. Professor Koch will continue his investigation of models relevant to the theory of critical phenomena. His second main emphasis is an analysis of disordered systems such as the Hopfield model and the Sherrington - Kirkpatrick model, which exhibit spin glass behavior for a certain range of parameters.