Abstract:  Conformal blocks are the fundamental building blocks of CFTs (parameterized by c) and play an important role in several areas of mathematical physics from random geometry to black hole physics.  Starting from the formulation of conformal blocks on the one-point torus by Promit Ghosal, Guillaume Remy, Xin Sun, Yi Sun (arxiv:2003.03802)., I will prove certain conjectures posed by Zamolodchikov regarding the semiclassical (c -> \infty) behaviour of conformal blocks and show their relation to the Lamé equation. This talk is based on a joint work with Promit Ghosal and Andrei Prokhorov (arXiv: 2407.05839).