Universal Random Structures in 2D
A graduate-level MIT OpenCourseWare course on the random objects that appear as universal scaling limits in two dimensions, including Schramm-Loewner evolution, the Gaussian free field, Brownian motion and its relatives, and models from statistical mechanics such as percolation. The course traces how these structures connect to one another, building toward the idea that many seemingly different random processes converge to the same limiting objects. Materials include lecture notes covering the theoretical development of each structure and discussion of open problems currently studied in probability theory. The course assumes strong background in probability and analysis and is aimed at graduate students working toward research in this area. As with most MIT OpenCourseWare offerings, materials are free to access online with no certificate offered, under a Creative Commons license permitting noncommercial reuse.