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COLLOQUIA

Classifying diffeomorphisms of surfaces 

Matthew Foreman (University of California, Irvine)

Location:  HILL 705
Date & time: Friday, 15 September 2017 at 4:00PM - 5:00PM

Abstract:  In 1932, von Neumann proposed classifying the statistical behavior of diffeomorphisms of manifolds. In modern language this means classifying diffeomorphisms that preserve a smooth volume element up to measure theoretic isomorphism. Despite important progress using entropy and spectral invariants, the general problem remained open. This talk proves that a complete classification is impossible in a rigorous sense—even on compact surfaces. The proof of the theorem involves producing new examples of diffeomorphisms with strong structural properties such as high distal rank.

 

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Department of Mathematics

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Rutgers University
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