Mathematical Sciences: The Conley Index: Theory and Applications

首席研究员将继续研究 连接矩阵该研究结合了代数方法， 几何学和微分方程的定性理论。 要研究的主题包括康利指数，弗洛尔同源性， 反应扩散方程的行波解 连接矩阵是一种装置，它制定了某些 偏微分方程的代数方面 框架.首席研究员将尝试开发 计算方法，利用代数 框架，从而获得更准确的质量信息， 微分方程。捕食者与被捕食者的问题 这一研究将被应用于的经典问题。

The principal investigator will continue his study of connection matrices. The research combines methods from algebraic geometry and the qualitative theory of differential equations. Topics to be studied include the Conley index, Floer homology, and traveling wave solutions to reaction diffusion equations. The connection matrix is a device which formulates certain aspects of partial differential equations in an algebraic framework. The principal investigator will attempt to develop computational methods which take advantage of the algebraic framework and thus obtain more precise qualitative information on the differential equations. The predator - prey problem will be one of the classical problems to which this research will be applied.