Stars at infinity in Teichm"uller space

For any metric space with a topological boundary, Anders
Karlsson defined subsets of the boundary called “stars at infinity,”
defined by intersection patterns of metric half-spaces. He used these
to prove dynamical theorems about groups acting by isometries, and he
made an attractive conjecture about the stars in the Thurston boundary
of Teichm"uller space. I will discuss joint work with Joseph Maher on
this conjecture, and explain various interesting consequences.