Mathematical Sciences: Applications of Numerical            Methods to Problems in Geometric Function Theory
{'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 seeks to develop further the methods and theory               of numerical techniques applied to the study of problems arising                in geometric function theory.  While the basic numerical methods                are generally available, their application to specific problems                 such as seeking global trajectory structures for quadratic                      differentials are far from perfected.  Many fundamental questions               can be reduced to those of solving for properties of a particular               conformal map which is known to satisfy a particular differential               equation.                                                                            These equations, the result of applying variational                        techniques to single out extremal functions, are of apparent                    simple type.  But the parameters they contain are defined by                    awkward side conditions.  This makes the equations into                         functional differential equations - equations which first                       appeared in the theory of automorphic functions and now occur in                the study of Riemann surface moduli and in various questions                    concerning ordinary differential equations of complex arguments.                     In addition to the development of general methods and,                     eventually, programs, work will be done on specific problem areas               where new approaches should flow from the computational                         development.  These areas include studies of the space of bounded               nonvanishing univalent functions defined in a disc.  This subject               has been the focus of intense research in recent years but now is               short of fresh new approaches to the resolution of many important               questions.  Work will also be done analyzing the class of                       univalent functions whose range covers a fixed disc.  Finally                   efforts will be made to sharpen upper and lower estimates for the               universal Bloch constants.  There is known to be considerable                   room for progress here.
{'FirstName': 'James', 'LastName': 'Hummel', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James A Hummel', 'EmailAddress': None, 'NSF_ID': '000444950', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Maryland, College Park', 'CityName': 'COLLEGE PARK', 'ZipCode': '207425100', 'PhoneNumber': '3014056269', 'StreetAddress': '3112 LEE BUILDING', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'MD04', 'ORG_UEI_NUM': 'NPU8ULVAAS23', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF MARYLAND, COLLEGE PARK', 'ORG_PRNT_UEI_NUM': 'NPU8ULVAAS23'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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