The correlation between shapes
In this talk, we explore the intricate relationships between diverse geometric
objects by leveraging tools from dynamical systems, within
the framework of the field known as ergodic geometry. Our primary
focus lies on the correlation number, a measurement that quantifies
the similarity between the “shapes” of two geometric entities. This
approach enables a comparative analysis of a wide spectrum of objects,
including (cusped) hyperbolic surfaces, networks, and (cusped)
Hitchin representations.