Description:

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

Participants:

We anticipate an audience of approximately 15 people, mostly graduate students and postdocs with the possibility of a few exceptional undergraduates. Due to grant restrictions, travel and lodging support is available only to U.S. citizens and permanent residents.

Applications:

Interested students should should submit a short CV and a summary of their qualifications and interest to:
ergdst@math.uci.edu

The deadline for applications is May 15, however late applications will still be considered on a case-by-case basis.

Schedule:

Week 1: The first week will treat positive classification results and associated tools. We will primarily focus 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). This will bring us to the forefront of current research.

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

A more detailed schedule will be posted at a later time.