Liouville Quantum Gravity as a Metric Space and a Scaling Limit
Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s. The second is the Brownian map, which has its roots in planar map combinatorics from the 1960s together with recent scaling limit results. In this talk, we will discuss the relationship between these objects in addition to how it can be used to study statistical mechanics models on random planar maps.
Parts of this talk will describe joint works with Ewain Gwynne and Scott Sheffield.