Title: Spherelike objects and quiver constructions

Abstract: The most simple kind of objects in a triangulated category are 
the exceptional objects. Next in complexity are objects with 2-dimensional 
graded endomorphism algebra; we call these "spherelike". In the first part 
of the talk, I will motivate why spherelike objects are interesting, and 
show examples occurring in derived categories of algebras.
In the second part, I will explain how spherelike objects can be collected 
in a new invariant of triangulated categories, the "spherelike poset". I 
will mention some concrete operations on quivers with relations for which 
we can track the growth of this poset.
(Joint with Andreas Hochenegger, Milano, and Martin Kalk, Edinburgh.)