Mathematical Sciences: Periods and Moduli Spaces
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research will center on two basic problems.  The main                 one involves the geometry of the period space.  In the first part               of this problem the P.I. will attempt to construct a smooth                     analytic compactification of period space in arbitrary weight.                  The boundary components should have an interpretation as period                 spaces for mixed Hodge structures and the gluing should reflect                 several fundamental results on degeneration of Hodge structures.                This compactification should make it possible to recast much of                 Hodge theory in a more geometric form and help in the study of                  Shimura varieties.  In the second part of this problem the                      Cartan-Kahler theory of regular integral elements for exterior                  differential systems will be applied to obtain dimension bounds                 and local invariants for the image of the period map as well as                 its intersection with Shimura varieties.  The second problem                    deals with moduli spaces of Lax structures.  Here the research                  will focus on the study of the moduli space of Lax structures for               a given integrable Hamiltonian system as the fundamental algebra-               geometric invariant of the system replacing the less natural                    though common notion of spectral curve.  Applications are                       envisaged to a series of classical systems in the form of theta-                function parametrizations which are completely natural to their                 systems rather than working only up to isogeny.                                      This research will focus on problems in algebraic geometry                 and applications to partial differential equations.  Not only                   then will the geometric objects arising as the set of solutions                 of simultaneous polynomial equations be studied for their own                   sake but attempts will be made to apply this deep theory to other
{'FirstName': 'Ron', 'LastName': 'Donagi', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ron Donagi', 'EmailAddress': 'donagi@math.upenn.edu', 'NSF_ID': '000094270', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Pennsylvania', 'CityName': 'PHILADELPHIA', 'ZipCode': '191046205', 'PhoneNumber': '2158987293', 'StreetAddress': '3451 WALNUT ST STE 440A', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'PA03', 'ORG_UEI_NUM': 'GM1XX56LEP58', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF THE UNIVERSITY OF PENNSYLVANIA, THE', 'ORG_PRNT_UEI_NUM': 'GM1XX56LEP58'}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8712298.xml'}