3:30–4:30 pm Maria Goeppert-Mayer Lecture Hall
Random Tilings
Alisa Knizel, University of Chicago
Random tiling models have been intensively studied in the last 25 years. In its simplest form, the random tiling model consists in the study of the set of tilings of a region (for example, a subset of the plane) with translated copies of a finite collection of shapes. But even the simplest cases have proved to be hard to analyze. However, in the few cases that are well-understood by now and that I will focus on (such as domino and lozenge tilings of planar domains), we find very rich behavior, with interesting enumerative properties, phase transitions and unexpected connections to different areas of mathematics.