$N=2$ Supersymmetric Field Theories, and Quivers, I

In these two lectures, I will review some of the relations between representation theory and the physics of $N=2$ supersymmetric gauge theories. In particular, I will discuss the concepts of gauge functor and perturbative (or light) subcategories, categorical Higgs mechanism, and categorical quantization. If time permits, I would like to discuss also the relation in between cluster algebras, Coxeter combinatorics and finite $N=2$ BPS mass spectra, and to formulate some of the open questions and conjectures. Based on joint work with S. Cecotti.