Mathematical Sciences: Analysis and Complex Geometry
{'Code': '03040108', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Lipman Bers, one of the founding fathers of Teichmuller                    theory, will continue his work on the strong deformation spaces                 of Riemann surfaces with nodes. He will attempt to extend the                   theory of Riemann surfaces with nodes to surfaces of infinite                   Poincare area. This is connected with the study of infinite                     dimensional deformation spaces and moduli spaces which are                      currently of interest to string theorists. He will also continue                his investigations of the complex boundaries of Teichmuller                     spaces.                                                                              Masatake Kuranishi's research will continue his work on the                sectional curvature of a certain metric on the cartesian product                of the two-sphere with itself. The objective is to deform this                  metric in such way as to obtain one of positive sectional                       curvature. If successful this will provide a positive answer to a               conjecture of Hopf. Kuranishi's second topic of investigation is                to bring the geometry of CR manifolds into the calculus of                      Fourier integral operators with complex phase on strongly                       pseudoconvex manifolds.                                                              Duong Phong will carry out research in two areas. These                    concern oscillatory integrals in Fourier analysis and the                       connections between string theory and Riemann surfaces. The                     former comprises an investigation of the role of geometry in the                study of singular kernels. The latter will be a continuation of                 earlier work in which Phong, together with collaborators, has                   identified the scattering amplitudes of strings with the Weil-                  Peterson measure on the moduli space.                                                Hubert Goldschmidt will work on problems in Riemannian                     geometry related to integral geometry and the deformation theory                of Riemannian metrics. In particular his research will be                       concerned with rigidity questions arising from the Blaschke                     problem for compact symmetric spaces. This will be studied in the               context of the Radon transform for tensors on these spaces.
[{'FirstName': 'Lipman', 'LastName': 'Bers', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Lipman Bers', 'EmailAddress': None, 'NSF_ID': '000163411', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Masatake', 'LastName': 'Kuranishi', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Masatake Kuranishi', 'EmailAddress': 'mk@math.columbia.edu', 'NSF_ID': '000309516', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Duong', 'LastName': 'Phong', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Duong H Phong', 'EmailAddress': 'phong@math.columbia.edu', 'NSF_ID': '000197362', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'Columbia University', 'CityName': 'NEW YORK', 'ZipCode': '100277922', 'PhoneNumber': '2128546851', 'StreetAddress': '615 W 131ST ST', 'StreetAddress2': 'MC 8741', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'NY13', 'ORG_UEI_NUM': 'F4N1QNPB95M4', 'ORG_LGL_BUS_NAME': 'THE TRUSTEES OF COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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