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Conformal blocks are fundamental ingredients of the conformal field theory and are closely related to supersymmetric gauge theory. They also have intimate connections with Painleve tau functions and limits of spiked random matrices.

In this talk, I will demonstrate a probabilistic construction of the 1-point torus conformal block using Gaussian multiplicative chaos and discuss some of its properties and connections. This talk will be based on joint works with Guillaume Remy, Xin Sun and Yi Sun.