This is SO COOL

“Dance your PhD”—yes, it’s a real thing

Every year, there is a competition called “Dance Your PhD” in which doctoral students choreograph dances that are meant to kinesthetically explain their dissertation. Seven years ago, this was the winner and it’s really, really cool. Dr. Scherich’s website is linked.

From the YouTube description:

On the surface, mathematics can seem rigid and colorless. But those who really look can see the deep beauty, elegance, and creativity with in mathematics. Let this video take you on a journey to view mathematics through the eyes of a mathematician. This aerial and contemporary dance interpretation describes the research of UCSB’s graduate student Nancy Scherich and her work with Representations of the Braid Groups. For a mathematician, a braid is a diagram of tangled strings. We can stack two braids on top of each other to make a new and longer braid. Braids can also interact with each other according to other specific rules called braid isotopy. As you might imagine, it is difficult to do “math” with diagrams of strings. So we go through a difficult translation process to turn the braids into a new form that is more comprehensible. A representation is the process of turning braids into matrices. A matrix is a grid of numbers and there are incredibly powerful theories and tools to study matrices. Learning about the matrices in turn gives us valuable informations about the braids we started with. However, not all representations accurately translate the braids. The braids that get lost in the translation process are called the kernel of a representation. We call a representation faithful if it only has one braid in its kernel. In other words, it faithfully translated the information. We call a representation unfaithful if it has more than one braid in its kernel. The main representation in the video wears a nametag that says Burau, n = 3. Burau is the name of a representation that is known to be faithful when n=3. Famously, no one knows if Burau for n = 4 is faithful or unfaithful, or rather, no one knows how many braids are in its kernel. My research is inspired by trying to answer this question for Burau n = 4.