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

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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.