The workshop will bring together two communities studying random planar geometry: one group studying Liouville quantum gravity and related topics, and a second studying random geometry in the Kardar-Parisi-Zhang universality class. The goal of the workshop is to foster connections between the two groups and to better understand the mathematical relationships between these two research areas. Sample topics for the workshop may include: properties of geodesics, the Robinson-Schensted-Knuth correspondence and its role in random geometry, Gaussian multiplicative chaos, models of random permutations and scaling limits, six vertex models, Yang-Baxter equations and integrability, the critical 2D stochastic heat flow, and connections to random matrices.