Mathematical Sciences: Problems in Conformal Field Theory

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Zuckerman will investigate topological conformal field theory. He will study the algebraic structures that are naturally defined in the state space of a TCFT. He will also investigate TCFT as a broad class of models that include the conformal string backgrounds. Khesin will continue to investigate the role of the Virasoro Lie algebra and Lie group in one dimensional fluid dynamics and two dimensional nonlinear wave propagation. He will also pursue his study of higher analogs of the Poisson bracket algebra associated to the Virasoro Lie algebra. 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.