Mathematical Sciences: The Conley Index and Applications to Physical Problems
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
James Reineck will continue the development of the theory of               the Conley index and the connection matrix. The fundamental                     objective is to use topological information to provide dynamical                information about flows. The Conley index generalizes the notion                of relative homology sequence of a filtration which has been                    studied in the past.                                                                 Reineck intends to apply this theory to problems in                        reaction-diffusion equations, chemical networks and ecology. The                problems in the theory of the index are the proof of a Poincare-                Hopf type theorem, the study of the relation between the indices                of a set in an invariant subspace and the index of the whole                    space, and development of an equivariant theory. Connection                     matrix problems include a relation between the connection map and               the topology of the set of connections, the development of a map                to describe families of connecting orbits in Morse decompositions               and a more complete understanding of the ambiguity which arises                 in the connection matrix.
{'FirstName': 'James', 'LastName': 'Reineck', 'PI_MID_INIT': 'F', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James F Reineck', 'EmailAddress': 'reineck@buffalo.edu', 'NSF_ID': '000318668', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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