|Analysis - Mathematical Physics|
|Topic:||Cardy embedding of random planar maps|
|Date:||Friday, December 6|
|Time/Room:||3:30pm - 4:30pm/Simonyi Hall 101|
A random planar map is a canonical model for a discrete random surface which is studied in probability theory, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2D Riemannian manifold with roots in the physics literature. In a joint work with Xin Sun, we prove a strong relationship between these two natural models for random surfaces. Namely, we prove that the random planar map converges in the scaling limit to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.