Random metric geometries on the plane and Kardar-Parisi-Zhang universality

Abstract

This is the article with the same title which is scheduled to appear in the January 2022 issue of the AMS Notices, with additional references which could not be provided in the accepted version due to space constraints. The figures in this article were made collaboratively with Milind Hegde.

16 pages, 5 figures, To appear in the January 2022 issue of AMS Notices