groupoid

The most common notion of symmetry in mathematics and its applications is associated with groups, for instance the rotations, reflections, and translations of the euclidean plane.    In recent years, a more general structure known as a groupoid has been found to provide a broader notion of symmetry.

I will explain what a groupoid is, will give some basic examples, and will tell about some subjects to which they have been applied, including dance patterns, the "15 Puzzle", networks of coupled systems, and patterns like the tiles on a floor.