Mathematical Sciences: Hodge Theory and L2-Cohomology
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Gary Cornell', 'PO_EMAI': None, 'PO_PHON': None}
This research is in the area of locally symmetric spaces and               the transcendental methods of algebraic geometry.  More                         specifically it will concentrate on the Hodge theory for the                    intersection homology of varieties.  These structures should be                 given simpler descriptions and they should be related to the                    Hodge structures provided by L2 harmonic forms with respect to                  good Kahler metrics.  A related development along these themes is               the appearance of two proofs of the principal investigator's 1980               conjecture equating the usual L2-cohomology of a locally                        symmetric variety with the intersection homology of its Baily-                  Borel-Satake compactification.  This problem will receive more                  work for the nature of the result will be elucidated by                         generalizing it to its natural setting, which is probably to                    Satake compactifications with only equal-rank boundary                          components.                                                                          The nature of this work is in the geometrical end of                       studying the sets of solutions of polynomial equations.  Various                invariants are studied which give deep understanding of these                   geometric objects.  These in turn should give applications to                   many areas of mathematics, most especially in geometry and                      analysis.
{'FirstName': 'Steven', 'LastName': 'Zucker', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Steven Zucker', 'EmailAddress': 'zucker@math.jhu.edu', 'NSF_ID': '000160066', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Johns Hopkins University', 'CityName': 'BALTIMORE', 'ZipCode': '212182608', 'PhoneNumber': '4439971898', 'StreetAddress': '3400 N CHARLES ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'MD07', 'ORG_UEI_NUM': 'FTMTDMBR29C7', 'ORG_LGL_BUS_NAME': 'THE JOHNS HOPKINS UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8800355.xml'}