The Quantum Mechanical Many-Body Problem and Statistical Mechanics

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The work that will be done under this award addresses fundamental problems in the physics and mathematics of many-body systems. There will be three main areas: (1) the development of a non-perturbative quantum electrodynamics that can deal properly with the bound states of atomic and condensed matter physics; (2) a continuation of the progress made recently to understand rigorously the ground states of low density Bose gases, especially the condensation phenomenon, which is a subject of much current experimental interest; (3) the study of the Hubbard model, which is now considered one of the cornerstones of correlated electron phenomena. Additionally, some topics in pure mathematics and partial differential equations will be addressed.