Bootstrapping N > 1 SCFTs

In this talk we will discuss the bootstrap program applied to four-dimensional N=2 and 3 superconformal field theories, with focus on analytical results. We start by a brief review of the superconformal bootstrap program and how to obtain a protected subsector captured by a two-dimensional chiral algebra. Then we describe the constrains this imposes on the space of allowed SCFTs, obtaining analytic bounds on anomaly coefficients