MA 237: Introduction to Tilings
Credits: 3:0
This course will be an introduction to the mathematical theory of tilings. The first part of the course will concern tilings of the Euclidean plane, and topics covered will include tilings by regular Euclidean polygons, Archimedean tilings, symmetry groups of planar tilings, substitution tilings, aperiodic tilings including the Penrose tiles and the hat tile. The second part of the course will concern tilings of the hyperbolic plane, including triangle groups, existence of weakly aperiodic tiles and semi-regular tilings. In the final part of the course, topics related to tilings on surfaces, conformal tilings, and higher-dimensional tilings (in Euclidean n-space and hyperbolic 3-space) will be discussed. Along the way, the course will cover the basic notions needed from Euclidean and hyperbolic geometry, group theory, topology, and the theory of Riemann surfaces.
Suggested books and references:
- Colin Adams, The Tiling Book, American Mathematical Society, 2022.