Craig Kaplan (University of Waterloo)
Title:聽Order and disorder in tilings and non-tilings
Abstract:聽In tiling theory, many deep questions arise from the subtle ways that the local information encoded in the boundaries of a set of shapes determines the long-range behaviour of the tilings those shapes admit. 聽I am particularly interested in three problems in this domain: Heesch's problem, which asks how many times a non-tiler may be surrounded by copies of itself; the isohedral number problem, which asks how many transitivity classes a shape may force upon its periodic tilings; and the (now resolved) einstein problem, which asks for a single shape that is forced to tile non-periodically. 聽I will discuss these problems, some of the mathematical and computational research that has been done to study them, and their generalizations to multiple shapes.
Venue: Hybride - PK-5115, Pavillon Pr茅sident-Kennedy, UQAM