As a mathematician (and not just any kind of mathematician – a PURE mathematician), I heard of the “Dance Your PhD” contest and immediately burst out laughing. As much as there is some nice pure mathematical dancing out there (see, for instance, this series of videos of different numerical sorting algorithms interpreted through dance), the idea that someone’s mathematical PhD research could be conveyed via bodily gyration was both fantastical and hilarious.
However, like any good scientist, I’m happy to be proved wrong and in this lovely clip (below), Dance Your PhD 2012 entrant (and pure mathematician) Diana Davis explains some lovely maths behind cutting sequences on the double pentagon, using a dance by Libby Stein. Full marks for use of hats.
The explanation of the theorem is pretty clear, and left me with a strong urge to find out what the full result is. The maths is explained in this paper, called “Cutting sequences, regular polygons, and the Veech group”.