In this talk, I will gently introduce the machinery of the holomorphic modular bootstrap. The primary idea of this program is to understand and classify 2d rational CFTs (RCFTs) by studying modular linear differential equations (MLDEs). There is a profound connection between the CFT data -- central charge, conformal weights -- and solutions of MLDEs. While MLDEs are notoriously hard to study, one can use a "hauptmodul" to bring them to the complex plane, where they turn into Fuchsian ODEs. These Fuchsian ODEs can be numerically solved, thus giving us the so-called modular S-matrix, which encodes crucial information about the CFT. The numerical estimate can be used in conjunction with Galois symmetry to pin down the exact entries of the modular S-matrix.
