Description:

A graduate summer school was held August 14 - 25, 2017 at the University of California at Irvine. The topic of the summer school was classification problems in ergodic theory. Lectures were given by Peter Burton (Caltech), Matt Foreman (UC Irvine), and Brandon Seward (Courant).

Participants:

We had approximately 15 participants, mostly graduate students and a few postdocs and exceptional undergraduates.

Conference Photos

Schedule:

Seminar Rooms: PDF
Video recordings of the lectures
Extra Materials: References for Week 1   Slides for Week 2

Week 1: The first week treated positive classification results and associated tools. We primarily focused on entropy theory, starting with the classical entropy theory for actions of countable amenable groups and ending with the quite recent developments of entropy theory for actions of countable non-amenable groups (in particular, sofic groups). [References]

Week 2: The second week was concerned with anti-classification results: results showing that classifications are not possible with countable resources. We began with a review of naive descriptive set theory and then discussed classification in this framework. We proceeded to show that the classification problem is not solvable for Z-actions, even of real analytic diffeomorphisms of the torus. Finally, we placed the classification problems in the hierarchy of analytic equivalence relations under Borel reducibility. [Slides]

We ended the summer school with a problem session: Conference Questions.