**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 Aaron Lauda, a mathematician from the University of Southern California, who shows us how to represent complicated expressions and equations using pictures. Enjoy! In fact, Aaron has provided more artwork at his website. Go check it out.

Aaron explains the motivation behind his paper with Mikhail Khovanov, “A diagrammatic approach to categorification of quantum groups I.” Here is the abstract to their paper:

To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify , where is the Kac-Moody Lie algebra associated with the graph.

While the video above is for a general audience, Aaron Lauda’s paper is not (it’s written for other mathematicians). However, high school students who think they are potential math geniuses may still enjoy looking at it to see what advanced theorems and proofs look like.

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©2015 Scott Baldridge and David Shea Vela-Vick

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