Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has roots in string theory and conformal field theory. The second is the Brownian map, which has roots in planar map combinatorics.
We show that the Brownian map is equivalent to Liouville quantum gravity with parameter $\gamma=\sqrt{8/3}$.
Based on joint work with Scott Sheffield.