Mathematical Sciences: Cohomology of Arithmetic Groups
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle'}
This research will be in the cohomology of arithmetic groups               and the related automorphic forms.  It will concentrate on three                areas.  The first is the generalized modular symbols and the                    ghost classes.  They will be studied via the representation                     theory of certain finite groups.  The second is the congruences                 between cohomology classes with different coefficient modules and               between the associated eigenvalues of the Hecke algebra.  This                  leads to construction of torsion cohomology from cusp forms.                    There is a conjectural link with large representations of the                   Galois group of the rational numbers.  The third area is a                      computer-aided calculation of cohomology groups.                                     This research contains an interesting blend of algebra and                 analysis which is used to study questions in number theory.  This               is an important and very deep study which the P.I. has been very                successful at in the past.  He will undoubtedly continue to                     produce striking results during the tenure of this award.
{'FirstName': 'Avner', 'LastName': 'Ash', 'EmailAddress': 'avner.ash@bc.edu', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701758.xml'}