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.