Workshop on Topology: Identifying order in complex systems

We will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further...

In two-dimensional grain structure, one observes that grains with a small number of sides tend to be surrounded by grains with a large number of sides, and vice-versa. The Law of Aboav--Weaire gives this observation a mathematical formulation, that...

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth', which provide a...