Intended Audience: Everyone, and especially teachers who want to show to their students a mathematician explaining the motivation behind their own research.

In this episode we meet Pallavi Dani, a mathematician here at Louisiana State University, who talks to us about using geometry to study problems in algebra and vice versa.

Pallavi discusses some ideas related to her paper with Anne Thomas, Divergence in right-angled Coxeter groups. She talks about her research on divergence functions in a way that young people can understand!  In particular, if you are a high school teacher, you can use the first example to start a discussion with your students.

After watching the video, you should be able to understand the first paragraph of the abstract to their paper:

Let W be a 2-dimensional right-angled Coxeter group. We characterize such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.

While the video above is for a general audience, Pallavi’s paper is not (it’s written for other mathematicians).  However, ambitious high-school students may still enjoy looking at it to see what advanced theorems and proofs look like.

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