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In-Person TalkÌý

Liouville theory was introduced by A. Polyakov in 1981 as the theory governing the conformal factor in the summation over all 2d RiemannianÌýmetrics. In recent years it has undergone extensive study in the probability community, and numerous conformal field theory (CFT) predictions have been establishedÌýat a mathematical level of rigor. In this talk we will first explain how one can use probability theory to rigorously define Liouville theory in theÌýpath integral approach. In the second part we will survey the main mathematical achievements of this program, including, proof of the DOZZÌýformula, the conformal bootstrap, properties of conformal blocks, and integration over moduli space. We will also attempt to highlight novelÌýintuitions and formulas coming from probability.