Craig Kaplan (University of Waterloo)

Title: Order and disorder in tilings and non-tilings

Abstract: 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.  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.  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 Président-Kennedy, UQAM