Title: Brieskorn spheres bounding rational balls

Abstract: I will discuss a construction of rational homology balls
bounded by two infinite families of Brieskorn homology
3-spheres. These Brieskorn spheres have non-trivial Rokhlin invariant
and so do not bound integral homology balls, and they are the first
new examples since the 1980's, when Fintushel and Stern constructed a
rational ball bounded by Sigma(2,3,7). I will also discuss some
related problems. This is joint work with Selman Akbulut.