Mathematical Sciences: Scattering 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}
The goals of this project are the analysis of certain                   problems in number theory, function theory and scattering                       theory.  Techniques to be used involve spectral theory of the                   Laplace-Beltrami operator acting on automorphic functions over                  a fundamental domain with a finite number of sides and of                       either finite or infinite volume.  The Laplace-Beltrami                         operator is central to all three fields representing an                         important concept worthy of concentrated study.                                         This work as well as that recently completed on explicit                expanders and Ramanujan graphs gives the best possible                          expanders; these are the building blocks for switching networks                 as well as sorting schemes.  A sharpened form of the Moser                      inequality for the projective plane and detailed estimates on                   the destruction of cusp forms under perturbation of the                         Laplacian (and thus the winding number of the determinant of                    the scattering matrix) on surfaces of finite volume are                         expected.
{'FirstName': 'Ralph', 'LastName': 'Phillips', 'PI_MID_INIT': 'S', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ralph S Phillips', 'EmailAddress': None, 'NSF_ID': '000183299', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Stanford University', 'CityName': 'STANFORD', 'ZipCode': '943052004', 'PhoneNumber': '6507232300', 'StreetAddress': '450 JANE STANFORD WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '16', 'CONGRESS_DISTRICT_ORG': 'CA16', 'ORG_UEI_NUM': 'HJD6G4D6TJY5', 'ORG_LGL_BUS_NAME': 'THE LELAND STANFORD JUNIOR UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
{'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': '8703241.xml'}