Mathematical Sciences: The Complex Geometry of Integrable Hamiltonian Systems

两位主要研究人员将研究可积性的几何方面的隔离，Toda方程的奇性分析和Bruhat胞格的分层，涉及球面中的常平均曲率环面的Sine-Gordon方程的解，以及与泊松括号的性质相关的泛包络代数。这个项目涉及哈密顿系统的深层性质。这些微分方程组特别描述了机械装置的运动。这样的装置必须同时保存能量和动量。近年来，各种代数方法以及Painleve可积性分析在理解这类系统方面取得了长足的进步。该项目将为这些发展做出贡献。

The two principal investigators will study the isolation of a geometric aspect of integrability, singularity analysis of Toda equations and stratification of Bruhat cells, solutions to the sine-Gordon equations involving constant mean curvature tori immersed in spheres, and the universal enveloping algebra associated with properties of Poisson brackets. This project concerns deep properties of Hamiltonian systems. These are systems of differential equations which describe in particular the motion of mechanical devices. Such devices must conserve both energy and momentum. Recently, various algebraic methods as well as Painleve analysis of integrability has been used to make considerable progress toward the understanding of such systems. This project will contribute to these developments.