Mathematical Sciences: Geometry and Analysis in Manifolds

一位资深研究员将分析李群哈密顿作用的谱不变量和辛不变量。在相关工作中，另一名高级研究员将研究一种新的算子和逆散射伪微分学。与这两位几何学家合作，博士后研究员将研究非交换代数的Connes- getzler形式主义和Connes的陈恩特征。我们将继续研究逆散射所引起的各种几何和解析问题。这个理论被用来解释反射信号。在地震学中，逆散射被用来重建油层或油藏的形状。其他应用包括声纳、雷达和X射线晶体学。

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.