Mathematical Sciences: Statistical Mechanics of Disordered Systems & Conformal Field Theory

Kupiainen将继续他对无序系统统计力学的研究。这个程序的目的是发展精确的重整化群方法来研究各种各样的这样的系统。这些包括洛伦兹气体型的经典系统和晶格版本，以及量子系统中的扩散。他还将继续以WZW模型为中心的共形场理论研究。现代物理学，量子力学和相对论，是二十世纪的产物。它牢固地建立在上个世纪对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础，统称为数学物理学，范围从控制粒子动力学的薛定谔算子的详细分析，到试图将四种已知力统一为单一理论的统一场论。

Kupiainen will continue his investigations of the statistical mechanics of disordered systems. The purpose of this program is to develop exact renormalization group methods to the study of a wide variety of such systems. These include classical systems of the Lorentz gas type and lattice versions thereof as well as diffusion in quantum systems. He will also continue his research in conformal field theory, centered around the WZW model. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.