Bootstrapping $4d$ $\mathcal{N}=2$ conformal theories

We review the conformal bootstrap approach to $4d$ $\mathcal{N}=2$ superconformal field theories (SCFTs), and how it constrains the space of allowed theories. From the landscape of $\mathcal{N}=2$ SCFTs we focus on the "simplest" interacting theory, an Argyres-Douglas theory, and approach it both with numerical bootstrap techniques and with the Lorentzian inversion formula. We conclude with an outlook for the prospects of approaching other Argyres-Douglas theories