Mathematical Sciences: Chern Characters and Correction Termsin Index Theory on Noncompact Manifolds
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': None, 'PO_EMAI': None, 'PO_PHON': None}
One of the most fundamental developments in modern science                has been the theory of quantum mechanics.  The attempt to                       understand both the physics and the underlying mathematics                      has led directly to current frontiers in two important areas                    of Modern Analysis, representation theory and operator                          algebras.  Representation theory is a means of exploiting the                   inherent physical symmetries, while the concept of operator                     algebras was invented to provide the correct framework for                      quantization.  Recently, there has been a great expansion in                    our understanding of the mathematics underlying quantization.                   Representation theory and operator algebras have been brought                   together recently in a powerful theory that centers around the                  celebrated Atiyah-Singer index theorem.  This evolving field is                 often referred to as noncommutative differential geometry. The                  representation theory enters in the group actions on locally                    symmetric spaces as well as the role  that singular algebraic                   varieties play  in representation theory.  Current advances point               to the movement from finite to infinite discrete groups and from                compact manifolds to noncompact singular varieties. These are                   tied together through the fact that smooth points of singular                   varieties often arise as quotients of actions of infinite                       discrete groups on noncompact manifolds.  The geometry of the                   space is reflected in the representation theory of the group and                analysis of differential operators on the noncompact manifold.                  These are the questions that address modern index theory.                              Professor Haskell is a young researcher who has mastered                 the broad range of mathematics necessary to contribute to this                  field.  The investigator's prior work, in part collaborative, has               laid a solid foundation for undertaking the following work.                     Professor Haskell will study the index theory of geometric                      elliptic Fredholm operators on noncompact manifolds.  He will                   then apply this research to equivariant index theory  of                        noncompact group actions, to index theory on the smooth parts of                algebraic varieties, and on locally symmetric spaces.
{'FirstName': 'Peter', 'LastName': 'Haskell', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter Haskell', 'EmailAddress': 'haskell@math.vt.edu', 'NSF_ID': '000283423', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'United States Naval Academy', 'CityName': 'ANNAPOLIS', 'ZipCode': '214025008', 'PhoneNumber': '4102932504', 'StreetAddress': '181 WAINWRIGHT RD', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'MD03', 'ORG_UEI_NUM': 'C3FJGE4ZRPD5', 'ORG_LGL_BUS_NAME': 'NAVY, UNITED STATES DEPARTMENT OF T', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8717186.xml'}