# A more functional bootstrap

The conformal bootstrap aims to systematically constrain CFTs based on crossing symmetry and

unitarity. In this talk I will introduce a new approach to extract information from the crossing symmetry

sum rules, based on the construction of linear functionals with certain positivity properties. I show

these functionals allow us to derive a class of optimal bounds on CFT data, and also act as an ideal basis

for obtaining other bounds numerically. Furthemore I will argue that special extremal solutions to