In this talk we will explore connections between theory of quivers and their representations and various quantities interesting from physicist's point of view. These quantities include: knots invariants and partition functions of integrable lattice models, combinatorial problems of lattice paths counting, amplitudes in topological string theories and WKB-like expansion of wave functions. The central role will be played by a certain generating series associated to a quiver. This series finds its place in physical quantities appearing in the aforementioned contexts. As a byproduct of this analysis we will also see that this generating series generalizes the q-hypergeometric functions.
Alexi Morin-Duchesne