T-structures
encode important cohomological information regarding triangulated
categories. Therefore the construction of t-structures is an
important problem. In this talk we consider a way to construct new
t-structures from old by taking the extension closure of aisles.
There are connections to the structure of the poset of (bounded)
t-structures. The main examples we will consider are tame
hereditary algebras, where we give an explicit combinatorial
criterion to ensure averaging is possible. We expect our
techniques will apply more generally to the bounded derived
categories of (tame) weighted projective lines. This is a report
on joint work with Nathan Broomhead and David Ploog.