
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 casebycase 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 nonamenable groups (in particular, sofic
groups). This will bring us to the forefront of current research.
Week 2: The second week will be concerned with anticlassification 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 Zactions, 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.

