Mathematical Sciences: Growth Functions and Geometry of     Groups
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
Plotnick plans to investigate relationships between                        combinatorial and geometric properties of certain groups, as                    reflected in their growth functions.  The main objects of study                 will be discrete groups such as hyperbolic groups, especially in                dimensions 2 and 3, and Coxeter groups.  Methods used will be                   combinatorial (attempting to generalize work of Floyd/Plotnick in               dimension 2), geometric (following Cannon), and homological                     (applying the theory of Kac-Moody Lie algebras, including Bruhat                decompositions and flag manifolds, to certain topologically                     interesting classes of Coxeter groups).  In particular, he seeks                to understand certain symmetry properties enjoyed by these growth               functions, and also the connection between growth functions and                 Euler characteristics of certain discrete groups.
{'FirstName': 'Steven', 'LastName': 'Plotnick', 'PI_MID_INIT': 'P', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Steven P Plotnick', 'EmailAddress': None, 'NSF_ID': '000202783', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'SUNY at Albany', 'CityName': 'Albany', 'ZipCode': '122220100', 'PhoneNumber': '5184374974', 'StreetAddress': '1400 Washington Ave MSC 312', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '20', 'CONGRESS_DISTRICT_ORG': 'NY20', 'ORG_DUNS_NUM': '152652822', 'ORG_LGL_BUS_NAME': 'RESEARCH FOUNDATION FOR THE STATE UNIVERSITY OF NEW YORK, THE', 'ORG_PRNT_DUNS_NUM': '020657151'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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