Mathematical Sciences: Research in Algebra and Algebraic    Number Theory
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle'}
This project supports fundamental and computational                        research in algebra, number theory and algebraic geometry. One                  of the principal investigators will study algebraic K-theory                    with a particular emphasis on determining the structure of                      group rings. Another principal investigator will work on                        extending the notion of motivic cohomology to arbitrary weights                 which is a significant problem in algebraic geometry. Work will                 also be done on the theory of p-adic fields. Problems                           concerning the extension of Buchberger theory and algorithms to                 rings which have complementary valuation rings will be                          considered. In addition, this project includes research on the                  relationship between projective varieties and syzygies, a study                 of Castelnuovo-Mumford regularity and its relationship to the                   complexity of standard Groebner bases and syzygies.                                  This project involves research on a wide variety of                        problems in algebra, algebraic computation and number theory.                   Although the research covers a wide breath of topics, there are                 large overlaps and interactions among the investigators on this                 project. This typifies a growing trend in mathematics of                        interaction with many diverse areas along with the use and                      study of computation.
{'FirstName': 'R. Keith', 'LastName': 'Dennis', 'EmailAddress': 'dennis@math.cornell.edu', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Cornell University', 'CityName': 'Ithaca', 'ZipCode': '148502820', 'PhoneNumber': '6072555014', 'StreetAddress': '373 Pine Tree Road', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY'}
[{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8802276.xml'}