# Mathematics Colloquium

#### Cardy embedding of random planar maps

**Speaker:**
Nina Holden, ETH Zurich

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, February 4, 2019, 3:45 p.m.

**Synopsis:**

Abstract: A random planar map is a canonical model for a discrete random surface which is studied in probability, 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.