# Robin Endelman

Mathematics & Statistics Department, University of the Fraser Valley

I am a mathematician (abstract algebra, representation theory), and when not doing mathematics, I am an excessive knitter. The design for this piece was born in 2003, while I was a post-doc, and the Yang Baxter equation (the subject of my thesis) was fresh in my mind. I am excited that now (only 10 years later!) I have been able to create it.

The colours chosen were inspired by this thematic year of the Mathematics of Planet Earth (MPE2013), to represent water, sun, and life on earth. The yarn company (Manos del Uruguay) was chosen for its commitment to sustainable development, local farmers and artisans, and fair trade. The fibre (Silk Blend) was chosen for its softness and comfort, as the scarf is meant to be worn!

A fashionable equation: the Yang Baxter scarf
Manos del Uruguay's Silk Blend (merino and silk, hand-dyed)
2013

This scarf depicts the Yang Baxter equation of statistical mechanics, a variation of which is the braid equation in algebra, or the 3rd Reidemeister (equivalence) move in knot theory. Assigning the numbers 1,2,3 to the colours blue, green, gold, respectively, the Yang-Baxter equation reads: R_12 R_13 R_23 = R_23 R_13 R_12, where R_ij denotes strand i crossing strand j -- the two sides of the equation being depicted on the two ends of the scarf, with equality represented by the middle portion.

For the equation to read correctly, the fabric needed to be double-sided. To create the two-sided fabric and traveling cables simultaneously, I introduced a hybrid of double-knitting and tubular knitting. As a result of this technique, the coloured strands are produced as embedded I-cords in the brown body of the scarf.