Line defects in $\mathcal{N}=2$ QFT and framed quivers

I will discuss a certain class of line defects in four dimensional supersymmetric theories
with $\mathcal{N}=2$. Many properties of these operators can be rephrased in terms of
quiver representation theory. In particular one can study BPS invariants of a new kind, the
so-called framed BPS states, which correspond to bound states of ordinary BPS states with
the defect. Such invariants determine the IR vev of line operators. I will discuss how these
invariants arise from framed quivers. Time permitting I will also discuss a formalism to study
these quantities based on cluster algebras.