Mathematical Sciences: Diophantine Equations, Diophantine   Approximation and Geometry
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research will study various problems in diophantine                   approximations and analytic number theory.  One of the main                     themes will be the study of solutions of certain diophantine                    equations which are known to have nontrivial solutions and                      therefore must have solutions of small height.                                       This Principal Investigator is an expert in the area of                    number theory which uses sophisticated analytic tools to answer                 questions about the integers and the rational approximations of                 real numbers.  He will carry forward these investigations in the                current research.  It is important in many problems to know that                it is possible to obtain solutions to certain equations for which               one has precise measures on how big the solutions are.  This will               be a major theme of the current research, although there are many               others in this broadly based research.  Much of great interest                  will result from this program.
{'FirstName': 'Jeffrey', 'LastName': 'Vaaler', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jeffrey D Vaaler', 'EmailAddress': 'vaaler@math.utexas.edu', 'NSF_ID': '000400691', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Texas at Austin', 'CityName': 'AUSTIN', 'ZipCode': '787121139', 'PhoneNumber': '5124716424', 'StreetAddress': '110 INNER CAMPUS DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '25', 'CONGRESS_DISTRICT_ORG': 'TX25', 'ORG_UEI_NUM': 'V6AFQPN18437', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF TEXAS AT AUSTIN', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701396.xml'}