**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. Here is 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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©2016 Scott Baldridge and David Shea Vela-Vick

Supported by NSF CAREER grant DMS-0748636 and NSF grant DMS-1249708