Mathematical Sciences: Topics in Ergodic Theory and         Dynamical Systems.
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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 of an                    underlying set or space, and the ultimate goal is to determine                  long-term behavior.                                                                     Professor Feldman is a leader in ergodic theory whose                   research has been highly influential.  His recent work has                      involved rigidity of flows on negatively curved manifolds,                      positive entropy for certain flows on Euclidean space, non-                     measure-preserving transformations and random walks, and                        amenable group actions and consequences for von Neumann                         algebras of operators.  The current proposal continues this                     ongoing research.  In particular, Professor Feldman will study                  problems related to horocycle and geodesic flows, Kakutani                      equivalence, recurrence for nonstationary processes, and                        ordered pairs of ergodic equivalence relations.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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