Mathematical Sciences: The Conley Index: Theory and Applications

首席研究员将继续他对连接矩阵的研究。该研究结合了代数几何和微分方程定性理论的方法。 要研究的主题包括康利指数、Floer 同调和反应扩散方程的行波解。 连接矩阵是在代数框架中表述偏微分方程某些方面的装置。首席研究员将尝试开发利用代数框架的计算方法，从而获得有关微分方程的更精确的定性信息。捕食者-被捕食者问题将是本研究将应用的经典问题之一。

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.