Mathematical Sciences: Topological Dynamics
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Ergodic theory is an active, central area of Modern                        Analysis.  Its origins lie in the theoretical formulation for                   classical statistical mechanics at the end of the nineteenth                    century.  The modern point of view derives from the profound                    mathematical theory of recurrence and ergodicity, as developed by               Poincare, Birkhoff, von Neumann and other giants earlier in this                century.  As the subject has evolved and sophistication                         continually increased, ergodic theory has acquired close                        relationships with other branches of mathematics, such as                       dynamical systems, probability theory, functional analysis,                     number theory, differential topology, and differential geometry,                and with applications as far ranging as mathematical physics,                   information theory, and computer design.  The principal objects                 of study in ergodic theory are transformations, or flows, on an                 underlying set or space, and the ultimate goal is to determine                  long-term behavior.                                                                    Professor Ellis is a leading expert in topological                       dynamics, which involves the study of continuous flows.  He is a                master of the abstract, transcendental viewpoint, using his                     special insights to obtain deep, fundamental results.  His                      recent work shows how to subsume much of ergodic theory under                   topological dynamics.  This equivalence of ergodic and                          topological properties effects a great unification by which                     general theorems from topological dynamics are carried over                     directly to measure theoretic situations, proofs are simplified,                and considerable generalization is obtained.  In his current                    project, Professor Ellis proposes to utilize his new viewpoint to               investigate many significant topics of major impact in ergodic                  theory and dynamical systems. These include Furstenberg's theory                of Poisson boundaries, Moore's ergodic theorem, and the                         Margulis-Mostow-Zimmer-Ratner rigidity type theorems for various                geodesic flows on manifolds.
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{'Name': 'University of Minnesota Saint Paul', 'CityName': 'Minneapolis', 'ZipCode': '554552000', 'PhoneNumber': '6126252435', 'StreetAddress': '450 University Gateway', 'StreetAddress2': '200 Oak Street SE', 'CountryName': 'United States', 'StateName': 'Minnesota', 'StateCode': 'MN', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MN05', 'ORG_UEI_NUM': None, 'ORG_LGL_BUS_NAME': None, 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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