Patterns and Disorder: How Random Can Random Be?
Bryna Kra, Northwestern University
2015, March 30
A tiled floor usually has regular, ordered patterns in it, even if the tiling may be very complicated. We will explore what it means for a mathematical object to be ordered or disordered. For example, do all geometric configurations have to contain patterns? Do large sets of numbers have to contain any patterns? We explore different notions of patterned and random sets, starting with simple, well-known patterns and ending with problems that mathematicians still don’t know how to solve.