Title: Proof of the DOZZ Formula
Abstract: 
    In 1994 Dorn and Otto and in 1996 independently Zamolodchikov and
    Zamolodchikov proposed a remarkable explicit expression, the so called DOZZ
    formula for the 3 point structure constants of the Liouville Conformal Field
    Theory (LCFT). LCFT is a building block of non-critical string theory and
    two dimensional quantum gravity and the DOZZ formula is the key to its
    integrability. Remarkably the LCFT strucure constants also give the Nekrason
    partition functions of four dimensional gauge theories. I will review a
    rigorous probabilistic construction of LCFT and sketch a proof of the DOZZ
    formula obtained together with R. Rhodes and V. Vargas.