Résumé :
I will discuss a particular class of framed quivers. The
motivation to study these quivers comes from physics, where they
describe so-called line defects in supersymmetric quantum field
theories. Physicists are interested in understanding certain BPS
states associated with these line defects. I will give a precise
description of these quantities in terms of certain enumerative
invariants associated with the framed quivers. The computation of
these invariants can be reduced to a purely combinatorial problem. If
time permits, I will also describe a connection with the theory of
cluster algebras and with certain integrable systems.