Mathematical Sciences: Regulators, Class Groups and Iwasawa Theory
{'Code': '03040104', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Bernard McDonald'}
This research will concentrate on three important problems                 in number theory.  The first will be to sharpen the lower bounds                known for regulators of number fields.  The second will be the                  study of the distribution of the Frobenius map acting on the                    Jacobians of hyperelliptic curves over a finite field and thereby               study the distribution of the divisor class groups of such                      curves.  This is connected with the Cohen-Lenstra conjecture in                 number fields.  The third problem is the study of the purely ring               theoretic properties that may govern the vanishing of the Iwasawa               mu-invariant.                                                                        This research will consider various problems in number                     theory.  Number theory is the study of the properties of the                    integers.  The proposer brings to bear a wide variety of tools to               perform this research.  Using analysis and geometry the study of                lower bounds of one of the crucial invariants in algebraic number               theory, the regulator, will be studied.  The study of the                       distribution of divisor class groups involves a study in                        probability concerning these geometric objects.  The problem on                 the Iwasawa involves a heavy use of algebra techniques.  The                    principle has a firm command of these diverse tools and will                    contribute a great deal to the theory.
{'FirstName': 'Eduardo', 'LastName': 'Friedman', 'EmailAddress': None, 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Pennsylvania', 'CityName': 'Philadelphia', 'ZipCode': '191046205', 'PhoneNumber': '2158987293', 'StreetAddress': 'Research Services', 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703591.xml'}