Mathematical Sciences: Some Spectral and Isospectral        Problems in Riemannian Geometry
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Peter Perry will work on two areas of spectral theory on                   Riemannian manifolds. These involve the scattering theory of                    manifolds of constant negative curvature and inverse spectral                   problems on compact Riemannian manifolds. These are geometric                   problems but the techniques to be employed will involve methods                 of mathematical physics. The first project will make use of the                 stationary scattering theory of elliptic operators invented for                 for the Schrodinger equation. The inverse spectral theory will                  employ techniques of partial differential equations.                                The first set of problems to be addressed concerns the                      spectral theory of the Laplace operator on a real hyperbolic                    manifold and its connections with the theory of discrete groups                 of hyperbolic isometries. Perry will concentrate on those                       manifolds which are quotients of hyperbolic space by a group of                 hyperbolic isometries. The work will involve investigations of                  the resolvent, eigenfunctions and scattering matrix of the                      Laplace operator on the hyperbolic space. It is hoped that this                 will be helpful in studying the Selberg trace formula and the                   Selberg zeta function of the isometry group.                                        He will also continue his study of isospectral metrics on a                 Riemannian manifold. By restricting attention to metrics in a                   conformal class, Perry, in joint work with Brooks and Yang has,                 extended some two-dimensional results to the three- and four-                   dimensional case. Attempts will be made to remove the restriction               to conformal classes and to find higher dimensional results.
{'FirstName': 'Peter', 'LastName': 'Perry', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter A Perry', 'EmailAddress': 'peter.perry@uky.edu', 'NSF_ID': '000316569', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Kentucky', 'CityName': 'LEXINGTON', 'ZipCode': '405260001', 'PhoneNumber': '8592579420', 'StreetAddress': '500 S LIMESTONE', 'StreetAddress2': '109 KINKEAD HALL', 'CountryName': 'United States', 'StateName': 'Kentucky', 'StateCode': 'KY', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'KY06', 'ORG_UEI_NUM': 'H1HYA8Z1NTM5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF KENTUCKY RESEARCH FOUNDATION, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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