Torus one-point correlation numbers in minimal Liouville gravity

Minimal Liouville gravity (MLG) is a conformal field theory that is a model of two-dimensional quantum gravity and is presumably equivalent to the Hermitian matrix model in the double scaling limit near the critical point. Verification of this equivalence at the level of correlators or partition functions is complicated by the complexity of analytical calculations from the conformal-field-theoretic side. I will describe a method that allows one to obtain analytical answers for single-point correlation numbers in MLG on the torus "from the first principles". The method uses the so-called "higher equations of motion" by Al. Zamolodchikov in the Liouville field theory, previously successfully applied to calculate correlators in the genus zero. The report is based on the joint work of 2210.14568 with V. Belavin.