Leigh Foster, University of Waterloo
Introduction to planar tilings
From tangrams to tessellations to brick pavers, we have many real life examples of tilings of a planar region. In this learning seminar, we will get a gentle introduction to the math behind these ideas, and over the course of the term will be able to answer the questions: Given a set of tiles, can we determine if a given region is tilable? If so, do we have more than one way of laying out the tiles? How can we know when a tiling does not exist? To answer these questions, we'll use techniques including counting and coloring arguments, height functions from a more topological point of view, and a combinatorial group-theoretic approach, among others. No previous knowledge is needed, and no outside work is required! Come and listen and ask questions - everyone is welcome, and interruptions are expected.
For our first meeting, we will discuss the basics of tilings. What does it mean to tile a region, and what are some ways that these questions arise in mathematics?
MC 5403