Abstract:
We will begin with a general introduction to dynamical systems with holes
and identify key questions and issues important to the subject.  We will
include a discussion of general escape rates and their relation to pressure
as well as conditionally invariant measures and issues of non-uniqueness.
 We will then specialize to see what can be proved for dispersing billiards
with holes and present a number of recent results in this context.  This
talk surveys joint work with a number of authors, including Lai-Sang Young,
Paul Wright, Henk Bruin and Ian Melbourne.