Mathematical Sciences: Geometry and Analysis in Manifolds

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One senior investigator will analyze spectral and symplectic invariants of Hamiltonian actions by Lie groups. In related work, a second senior investigator will study a new pseudo-differential calculus of operators and inverse scattering. Working with these two geometers, a post doctoral investigator will study the Connes-Getzler formalism and Connes' Chern character for non- commutative algebras. Work will proceed on a variety of geometric and analytic problems which arise from the study of inverse scattering. This theory is used to interpret reflected signals. In seismology, inverse scattering is used to reconstruct the shape of oil or water reservoirs. Other applications include sonar, radar, and X- ray crystallography.