Mathematical Sciences: Arithmetic on Elliptic Curves and    Related Topics
{'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 be on problems related to the question of               supersingular primes for a given elliptic curve over a number                   field.  Immediate goals include a proof of a natural sufficient                 condition for the infinitude of supersingular primes in the                     totally imaginary case and unconditional explicit lower bounds on               the density of such primes.  Further goals will include the                     nonzero fixed trace problem (of which many old classical problems               are special cases) and various other open problems in the                       arithmetic of elliptic curves and abelian varieties of higher                   dimension.                                                                           The area of this research is in that branch of number theory               which studies certain cubic equations and the number of rational                solutions of them (elliptic curves).  The subject has connections               throughout mathematics and has been instrumental in solving many                problems in number theory concerning many topics.  The number of                solutions of the equation modulo primes is a central focus in the               subject and this is the area focused on by this investigator.
{'FirstName': 'Noam', 'LastName': 'Elkies', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Noam Elkies', 'EmailAddress': 'elkies@math.harvard.edu', 'NSF_ID': '000171953', 'StartDate': '12/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Harvard University', 'CityName': 'CAMBRIDGE', 'ZipCode': '021385366', 'PhoneNumber': '6174955501', 'StreetAddress': '1033 MASSACHUSETTS AVE STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MA05', 'ORG_UEI_NUM': 'LN53LCFJFL45', 'ORG_LGL_BUS_NAME': 'PRESIDENT AND FELLOWS OF HARVARD COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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