Mathematical Sciences: The Laplacian in Hyperbolic Space andEntropy in Dynamical Systems
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Thea Pignataro will carry out research in two areas. The                   first concerns the spectral theory of three dimensional manifolds               and the second focusses on estimation of the topological entropy                in dynamical systems. The spectral theory of manifolds centers                  around the derivation of geometric information from knowledge of                the spectrum of the Laplacian on the manifold. This has its                     origins in questions such as "Can you hear the shape of a drum?",               since the spectrum of the Laplacian is closely related to the                   harmonics of the surface. Her work on entropy is part of a wide                 ranging program of many researchers to measure the chaos in a                   system.                                                                              Pignataro has already been involved in important work on the               eigenvalues of the Laplacian on hyperbolic surfaces. The results                there show that the small eigenvalues vary like the lengths of                  short separating geodesics. The more complicated the topology the               more eigenvalues that can be estimated. She will now try to                     extend some of these ideas and results to three dimensional                     manifolds. This will involve overcoming quite difficult                         topological problems. In particular the ends of these manifolds                 are more complicated than those of surfaces and have only                       recently been understood.                                                            Her work on dynamical systems involves estimation of the                   topological entropy. This essentially measures the number of                    different orbit types of a system. She will investigate the                     connections between entropy and the volume growth of certain                    embedded submanifolds.
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{'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': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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