Non-classifiability of K-automorphisms - Lecture on Measure-Preserving Transformations

Explore a 53-minute lecture on the non-classifiability of K-automorphisms, presented by Marlies Gerber from Indiana University as part of the Simons Semester on Dynamics. Delve into the complexities of measure-preserving transformations, focusing on K-automorphisms and their mixing properties. Learn about the impossibility of classifying K-automorphisms using a complete numerical Borel invariant, and discover the proof that the isomorphism equivalence relation restricted to K-automorphisms is complete analytic. Examine topics such as the weak topology on MPT's, Borel reduction of equivalence relations, von Neumann's classification problem, and the construction methods for K-automorphisms. Investigate related concepts including first return maps, special flows over transformations, Even Kakutani Equivalence, and basics of Descriptive Set Theory. Gain insights into the canonical example of a complete analytic set and the non-classifiability of smooth K-diffeomorphisms in this comprehensive exploration of advanced mathematical concepts.

Intro
The Isomorphism Problem
Weak Topology on MPT's
What is meant by a classification?
Borel Reduction of Equivalence Relations
Another benchmark: The equivalence relation =+
Borel Equivalence Relations
von Neumann's classification problem is impossible
Several further questions
K-automorphisms
First return map
Some methods for constructing K automorphisms
Classification for Generic Subsets of MPT's
Special flows over a transformation
Even Kakutani Equivalence
Anti-classification results for Kakutani equivalence
Basics of Descriptive Set Theory
Example of an analytic set
Canonical example of a complete analytic set
Non-classifiability of Smooth K-Diffeomorphisms