9401735 Shubin This proposal concerns problems from inverse spectral theory and random Schrodinger operator theory. The problems proposed in the inverse spectral theory section center around recovering certain types of singularities of the potential of a Schrodinger operator from the set of eigenvalues. The problems from random Schrodinger operator theory concern localization in d-dimensional Euclidean space for Anderson and Poisson type models. Modern physics, quantum mechanics and relativity is a product of the twentieth century. It is founded firmly in the attempt to address the microstructure of matter and to come to grips with the concept 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 Schrodinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory. This project is focused on the Schrodinger operator component of mathematical physics research. ***
