Ethan Dlugie (Brown University)

Abstract

A mosaic in a house of worship, a wall in a 1960s American home, the tiling on a bathroom floor; all of these human creations exhibit our innate fascination with repeating visual patterns. But as mathematicians, we don't simply marvel at visual beauty, we seek to understand it! How many of these repeating planar patterns are there? What are their mathematical features? How do we classify them? In this talk, we'll discuss how all of these questions can be answered with an inspiring blend of tools from algebra, geometry, and topology. No background is required, and there will be pictures aplenty.