The PNAS journal, which is celebrating its 100th anniversary in 2015, has recently published a paper entitled Knot theory realizations in nematic colloids, by Simon Čopar, Uroš Tkalec, Igor Muševič and Slobodan Žumer from the Faculty of Mathematics and Physics in Ljubljana, the Faculty of Natural Sciences and Mathematics in Maribor, and the Solid State Physics Department of the Jožef Stefan Institute.
The authors report diverse applications of knot theory in nematic liquid-crystal colloids with knotted defect loops. The results demonstrate how the construction of graphs, topological surfaces and knot polynomials is showcased directly on experimental micrographs, thereby identifying the entangled structures without the need for numerical simulations. The paper illustrates how abstract mathematical concepts manifest elegantly as observable features in soft-matter physics.