| Abstract |
In this talk, I will survey Liouville quantum gravity (LQG) surfaces in the supercritical regime, where the matter central charge exceeds 1. Unlike the subcritical case---where many models from mathematical physics (such as percolation and Ising) are known to converge to LQG surfaces---no canonical model is currently available in this regime. I will discuss how the six-vertex model may serve as a candidate whose scaling limit is a supercritical LQG surface, and I will present some preliminary progress and many conjectures in this direction, based on joint work with Ewain Gwynne and Andrew Elvey Price. |
