Over the past several 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 from the 1980s and 1990s. The second is the Brownian map, which has roots in planar map combinatorics from the 1960s.

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.