Mathematical Sciences: Variational Methods and Quadratic    Differentials
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This project will be concerned with problems related to                 analytic functions of a complex variable and associated                         geometric questions.  The principal investigator is                             particularly concerned with univalent functions defined in a                    disc or in the exterior of a disc.  By virtue of their                          analyticity, these functions have power series expansions in                    the variable or its reciprocal.  Objectives of this work                        include the analysis of extremal problems in terms of the                       series coefficients and a description of the image boundary for                 extremal maps.  Techniques to be used involve methods of                        extremal metrics and quadratic differentials (techniques which                  are actually closely related)  The principal investigator has                   displayed considerable expertise in using these methods in his                  past work.                                                                              The coefficient function of the quadratic differential                  often gives precise information concerning the boundary image                   of an extremal map.  Work will be done investigating this                       function further.  In particular, the principal investigator                    will seek to establish whether or not this function must have                   simple roots.  A new direction of research undertaken by the                    principal investigator focuses on iteration of analytic maps                    and Julia sets.  These are sets representing the infinite past                  history of points carried by mapping iterates.  Evidence                        suggests an interesting connection between the nature of Julia                  sets (simple or extremely irregular) and the decay of                           coefficients of univalent mappings.  Work on such questions is                  still at the computer-experimental stage but appears to hold                    promise for interesting and unexpected relationships with                       dynamical systems.
{'FirstName': 'Yuk', 'LastName': 'Leung', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Yuk J Leung', 'EmailAddress': None, 'NSF_ID': '000468870', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Delaware', 'CityName': 'NEWARK', 'ZipCode': '197160099', 'PhoneNumber': '3028312136', 'StreetAddress': '220 HULLIHEN HALL', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Delaware', 'StateCode': 'DE', 'CONGRESSDISTRICT': '00', 'CONGRESS_DISTRICT_ORG': 'DE00', 'ORG_UEI_NUM': 'T72NHKM259N3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF DELAWARE', 'ORG_PRNT_UEI_NUM': 'T72NHKM259N3'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701472.xml'}