Mathematical Sciences: Topics in Analysis
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Professor Sarnak's research will be in the spectral theory                 of automorphic forms with applications to number theory,                        combinatorics and mathematical physics.  Two of the unsolved                    problems in this area which he plans to work on are (1) The                     existence of Maass cusp forms for nonuniform lattices and (2) The               "hearing the shape of a drum" problem, i.e. what can be said                    about an isospectral set of manifolds.  Professor Osgood will                   work on several problems in geometric function theory, some in                  joint work with Sarnak.  This work will concern the isospectral                 problem for surfaces with a generalization of the classical                     Schwarzian derivative to higher dimensions.                                          This research will involve a combination of geometry and                   analysis with applications to other areas of mathematics.  It                   turns out that the theory of automorphic forms, a subject arising               originally from number theory often as generating functions for                 arithmetic functions, has many applications to other areas.  This               theory is one of the main focuses of this research.
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{'Name': 'Stanford University', 'CityName': 'STANFORD', 'ZipCode': '943052004', 'PhoneNumber': '6507232300', 'StreetAddress': '450 JANE STANFORD WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '16', 'CONGRESS_DISTRICT_ORG': 'CA16', 'ORG_UEI_NUM': 'HJD6G4D6TJY5', 'ORG_LGL_BUS_NAME': 'THE LELAND STANFORD JUNIOR UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}, {'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}, {'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}]
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