Short talk: First order asymptotic of Liouville four-point correlation function and the conformal bootstrap

Based on the rigorous path integral formulation of Liouville conformal field theory introduced by David-Kupiainen-Rhodes-Vargas, we compute the first order asymptotic of the four-point correlation function on the sphere as two insertions get close together, which is expected to describe the density of vertices around the root of large random planar maps. Moreover, our results are consistent with predictions from the framework of theoretical physics known as the conformal bootstrap, featuring the DOZZ formula and logarithmic corrections in the distance between the insertions.