Mathematical Sciences: Ergodic Theory, Groups and Geometry
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This ambitious mathematical research project has to do with                actions of Lie groups, and certain of their discrete subgroups,                 on manifolds.  A very simple example of this situation is the                   group of rotations of three-dimensional space about axes passing                through the origin, acting on a sphere centered at the origin.                  In higher dimensions, the examples become more exotic, and more                 importantly, as Professor Zimmer has discovered, the rules of the               game that say what sorts of actions can occur on what sorts of                  manifolds change in striking and fundamental ways.  A whole new                 subject, which might be called nonlinear representation theory,                 is growing up to take its place next to the older and much better               understood theory of group representations on vector spaces.                    This research impinges directly on four core areas of                           mathematics: analysis, geometry, algebra, and topology.                              More specifically, Professor Zimmer will investigate the                   topology of manifolds admitting an action of a semisimple Lie                   group or discrete subgroup by describing features of the                        representation theory of the manifold's fundamental group.  The                 arithmetic nature of actions of of these groups will be                         investigated.  There will be continued study of the phenomena                   alluded to above that make the higher-dimensional case                          qualitatively different from the lower-dimensional.
{'FirstName': 'Robert', 'LastName': 'Zimmer', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robert J Zimmer', 'EmailAddress': 'zimmer@math.uchicago.edu', 'NSF_ID': '000185826', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606375418', 'PhoneNumber': '7737028669', 'StreetAddress': '5801 S ELLIS AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'IL01', 'ORG_UEI_NUM': 'ZUE9HKT2CLC9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CHICAGO', 'ORG_PRNT_UEI_NUM': 'ZUE9HKT2CLC9'}
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[{'Code': '1262', 'Text': 'MODERN ANALYSIS'}, {'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}]
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