Global conformal blocks on torus and Casimir equation

We consider the global blocks on the torus in a special "necklace" channel. First we repeat how these blocks generate global blocks with an arbitrary channel topology and derive the Casimir equations for these blocks. Then we will discuss the simplest cases where such blocks can be explicitly computed and verify that they satisfy the Casimir equations. The talk is based on the papers arXiv:2205.05038 and arXiv:2302.10153.