##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Philipp Kunde

#### University of Hamburg

## Anti-classification results for the Kakutani equivalence relation

##### Abstract:

Dating back to the foundational paper by John von Neumann, a fundamental theme in ergodic theory is the \emph{isomorphism problem} to classify invertible measure-preserving transformations (MPT's) up to isomorphism. In a series of papers, Matthew Foreman, Daniel Rudolph and Benjamin Weiss have shown in a rigorous way that such a classification is impossible. Besides isomorphism, Kakutani equivalence is the best known and most natural equivalence relation on ergodic MPT's for which the classification problem can be considered. In joint work with Marlies Gerber we prove that the Kakutani equivalence relation of ergodic MPT's is not a Borel set. This shows in a precise way that the problem of classifying such transformations up to Kakutani equivalence is also intractable.

Host: Brandon Seward

### May 18, 2021

### 10:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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