The consequences of the constraints of conformal symmetry are far-reaching withintheoretical physics. In this dissertation we address a series of questions in conformalfield theory: 1) We calculate the spectrum of qKdV charges in a large central chargeexpansion. 2) We determine the corrections to bulk information geometry from 1/Ncontributions to holographic correlators. 3) We study the higher genus partitionsfunctions of CFTs associated with classical and quantum error-correcting codes
