Mathematical Sciences: The Conley Index: Theory and Applications
James Reineck Principal Investigator
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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.