Mathematical Sciences: Geometry of the Fundamental Group
{'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}
Robert Brooks will investigate connections between the                     geometry of a surface and the eigenvalues of the Laplacian. Work                on these problems was popularized some years ago by questions                   such as "Can you hear the shape of a drum?". If you have perfect                pitch then you can in theory detect the harmonics of the drum,                  that is the eigenvalues of the Laplacian. So the question is how                much geometry of a surface can be detected from knowledge of                    these eigenvalues.                                                                   Brooks' work will focus on the study of the small                          eigenvalues of hyperbolic manifolds and isospectral problems on                 compact manifolds. There are already estimates for the low                      eigenvalues of compact manifolds. Brooks will work to extend                    these to the finite volume case. This is a non-trivial extension                but certainly a natural one since a key ingredient of earlier                   estimates is the the notion of injectivity radius which is zero                 for non-compact finite volume manifolds. His work on isospectral                problems is concerned with a study of the topology of sets of                   isospectral metrics in a given conformal class. The intention                   here is to apply the solution of the Yamabe problem to the                      geometry of three dimensional manifolds.
{'FirstName': 'Robert', 'LastName': 'Brooks', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robert Brooks', 'EmailAddress': 'rbrooks@mtha.usc.edu', 'NSF_ID': '000475663', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Southern California', 'CityName': 'LOS ANGELES', 'ZipCode': '90033', 'PhoneNumber': '2137407762', 'StreetAddress': '3720 S FLOWER ST FL 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '34', 'CONGRESS_DISTRICT_ORG': 'CA34', 'ORG_UEI_NUM': 'G88KLJR3KYT5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF SOUTHERN CALIFORNIA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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