Mathematical Sciences: Differential Geometry
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Daniel Freed will continue his work in differential geometry               concentrating on areas having significance in mathematical                      physics. In fact this is an area which in recent years has had                  great influence in topology. Ji-Ping Sha will investigate the                   topological consequences of various curvature restrictions on                   manifolds. He will also investigate applications of the Atiyah-                 Singer index theorem in Riemannian geometry.                                         Freed's previous work on the geometry of the determinant                   bundle associated to the Dirac operator has been very                           influential. He will continue to study this and in particular                   calculate the first Chern class of the determinant line bundle.                 He will also work to gain geometric understanding of the various                new cohomology theories which are currently being used to great                 effect in topology. Sha will continue his work on the topology                  and geometry of Riemannian manifolds with non-negative curvature.               Together with Yang, he has established some quite striking                      results and will now work towards a topological classification of               simply connected closed four and five dimensional manifolds with                positive Ricci curvature.
{'FirstName': 'Melvin', 'LastName': 'Rothenberg', 'PI_MID_INIT': 'G', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Melvin G Rothenberg', 'EmailAddress': None, 'NSF_ID': '000278122', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606375418', 'PhoneNumber': '7737028669', 'StreetAddress': '5801 S ELLIS AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'IL01', 'ORG_UEI_NUM': 'ZUE9HKT2CLC9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CHICAGO', 'ORG_PRNT_UEI_NUM': 'ZUE9HKT2CLC9'}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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