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The conformal bootstrap in D dimensions is known for its spectacular numerical results. In this talk I will go in a different direction and revisit the CFT landscape through the lens of Sturm-Liouville theory. I will discuss how conformal data (involving spectra, OPE coefficients, boundary and crosscap states) are naturally governed by integral equations. These can be thought of as the higher-D analog of sewing conditions in 2d RCFTs. Our integral equations are related to known objects in the mathematics literature, which allows us to find some mean-field solutions. Partially based on 1702.08471 with B. van Rees.

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