Mathematical Sciences: The Topology of Certain Algebraic    Varieties, and Applications
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
This research project involves application of the methods of               algebraic and differential topology to the study of certain                     algebraic varieties.  Weintraub will use a number of techniques                 and, in particular, exploit the fact that the spaces studied                    often admit, or arise from, certain natural group actions.  The                 varieties to be studied include the Igusa compactifications of                  degree two Siegel modular spaces corresponding to various                       congruence subgroups of the symplectic group of degree four (and                related groups), moduli spaces of Riemann surfaces (sometimes                   with special or additional structure), ball quotients, and other                varieties related to configuration spaces.  The information to be               obtained includes homology and cohomology (both the groups and                  geometric representatives of the classes), Hodge decompositions,                representations of the groups which act on the (co)homology,                    intersection homology, zeta functions, and Lefschetz numbers.  In               addition there are applications to group cohomology and Siegel                  modular forms.                                                                       One of Weintraub's techniques of interest in its own right,                is an elaboration of the Tits building (called "scaffolding")                   which he has developed.  Of particular interest is the                          application of this work to theta-functions.  It clarifies some                 points about how theta-functions transform, and most                            interestingly of all, reveals hitherto unsuspected connections                  between geometry/topology (in the guise of holonomy/Rochlin                     invariants) and theta-functions, and raises interesting new                     questions about the latter.  (The project represents a                          continuation of a long-running research program, much of it joint               work with other mathematicians.)
{'FirstName': 'Steven', 'LastName': 'Weintraub', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Steven H Weintraub', 'EmailAddress': 'shw2@lehigh.edu', 'NSF_ID': '000151978', 'StartDate': '10/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Louisiana State University', 'CityName': 'BATON ROUGE', 'ZipCode': '708030001', 'PhoneNumber': '2255782760', 'StreetAddress': '202 HIMES HALL', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Louisiana', 'StateCode': 'LA', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'LA06', 'ORG_UEI_NUM': 'ECQEYCHRNKJ4', 'ORG_LGL_BUS_NAME': 'LOUISIANA STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'Z7ZNZH7LJ778'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8803552.xml'}