Mathematical Sciences: Topological Classification of        Singularities and Nonlinear Problems
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
A number of fundamental questions about singularities of                   smooth mappings have been answered by John Mather using ideas                   proposed by Rene Thom.  This Thom-Mather approach solves the                    problems by reducing them to infinitesimal problems which can be                solved algebraically.  Unfortunately, this approach cannot be                   applied to the analogous topological problems.                                       James Damon has been developing a topological analogue of                  the Thom-Mather approach.  This has enabled him to obtain answers               to the topological questions in a number of circumstances.                      Likewise, he has been applying results from singularity theory to               obtain results about solutions to nonlinear differential                        equations.                                                                           He intends further to develop ideas on topological                         equivalence in singularity theory, to investigate the use of                    symbolic computations in addressing these questions, and to                     explore further the applications of singularity theory to                       nonlinear differential equations.
{'FirstName': 'James', 'LastName': 'Damon', 'PI_MID_INIT': 'N', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James N Damon', 'EmailAddress': 'jndamon@math.unc.edu', 'NSF_ID': '000235353', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of North Carolina at Chapel Hill', 'CityName': 'CHAPEL HILL', 'ZipCode': '275995023', 'PhoneNumber': '9199663411', 'StreetAddress': '104 AIRPORT DR STE 2200', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'North Carolina', 'StateCode': 'NC', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'NC04', 'ORG_UEI_NUM': 'D3LHU66KBLD5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL', 'ORG_PRNT_UEI_NUM': 'N8DMK1K4C2K5'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1267', 'Text': 'TOPOLOGY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8800824.xml'}